1

Kazuhiro Yamamoto

Henning Kaufer Tobias Westphal Daniel Friedrich Helge Mueller-Ebhardt

Stefan Gossler Karsten Danzmann and Roman SchnabelMax-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut)

Institut fuer Gravitationsphysik Leibniz Universitaet Hannover

Radiation Pressure NoiseExperiment in Hannover

Kentaro SomiyaWaseda University

Farid Y Khalili Stefan L DanilishinMoscow State University

19 May 2010 Gravitational-Wave Advanced Detector Workshop Hearton Hotel Kyoto Kyoto Japan

0AbstractRadiation pressure noise measurement

with extremely light

but translucent mechanical oscillator

New topology Michelson-Sagnac interferometer

Theoretical outlines

Current status of experiment

Future work

2

3

CLIO-MQM (Cryogenic Laser Interferometer Observatory-Macroscopic Quantum Measurement)

Workshop

24th and 25th May

Waseda Institute for Advanced Study Tokyo Japan

SL Danilishin ldquoTowards mechanical non-Gaussian

states with optical interferometersrdquo

FY Khalili ldquoUp-converter regime in the membrane

experimentsrdquo

K Yamamoto ldquoNano-gram membrane experiment

at AEIrdquo

Related talks

Contents

1 Introduction

2 Current status

3 Future work

4 Summary

4

1Introduction Interferometric gravitational wave detector

Current First generation (LIGOVIRGOGEOTAMACLIO)

Future Second generation

(GEO-HF Advanced LIGO and VIRGO

LCGT AIGO)

Third generation (Einstein Telescope)

Quantum noise Limit of future interferometer

Shot noise Phase fluctuation

Radiation pressure noise Amplitude fluctuation

5

6

1 IntroductionRadiation pressure noise (1)

httpspacefilesblogspotcom

Photons come at random (amplitude fluctuation) Back action of photon is also at randomrarr Radiation pressure noise

7

shot noise

quantum radiation pressure noise

standard quantum limit

quantum noise with 100x increased laserpower

1 Introduction Standard Quantum Limit

Nobody observed radiation pressure noise

Large radiation pressure noise

High laser power Light mass

~ m12

~ P12

~ P-12

Standard Quantum Limit (SQL) is a fundamental limit for

naively optimized conventional interferometers

8

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

Optical properties

Power Reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

1 IntroductionMichelson-Sagnac interferometer(1)

9

Membrane

From laser source

Beamsplitter

Steering mirror

Steering mirror

1 Introduction　 Michelson-Sagnac interferometer(2)

10

Sagnac mode

Michelson mode

Anti symmetric port (no light of Sagnac mode)

Symmetric port

Membrane position is adjusted to keep this port dark

11

1 Introduction Michelson-Sagnac interferometer(3)

Steering mirror

Steering mirror

Membrane

Beamsplitter

Laser source

Power recyclingmirror

Signal recycling mirror

Recycling techniques are useful even if the membrane reflectance is low

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

0AbstractRadiation pressure noise measurement

with extremely light

but translucent mechanical oscillator

New topology Michelson-Sagnac interferometer

Theoretical outlines

Current status of experiment

Future work

2

3

CLIO-MQM (Cryogenic Laser Interferometer Observatory-Macroscopic Quantum Measurement)

Workshop

24th and 25th May

Waseda Institute for Advanced Study Tokyo Japan

SL Danilishin ldquoTowards mechanical non-Gaussian

states with optical interferometersrdquo

FY Khalili ldquoUp-converter regime in the membrane

experimentsrdquo

K Yamamoto ldquoNano-gram membrane experiment

at AEIrdquo

Related talks

Contents

1 Introduction

2 Current status

3 Future work

4 Summary

4

1Introduction Interferometric gravitational wave detector

Current First generation (LIGOVIRGOGEOTAMACLIO)

Future Second generation

(GEO-HF Advanced LIGO and VIRGO

LCGT AIGO)

Third generation (Einstein Telescope)

Quantum noise Limit of future interferometer

Shot noise Phase fluctuation

Radiation pressure noise Amplitude fluctuation

5

6

1 IntroductionRadiation pressure noise (1)

httpspacefilesblogspotcom

Photons come at random (amplitude fluctuation) Back action of photon is also at randomrarr Radiation pressure noise

7

shot noise

quantum radiation pressure noise

standard quantum limit

quantum noise with 100x increased laserpower

1 Introduction Standard Quantum Limit

Nobody observed radiation pressure noise

Large radiation pressure noise

High laser power Light mass

~ m12

~ P12

~ P-12

Standard Quantum Limit (SQL) is a fundamental limit for

naively optimized conventional interferometers

8

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

Optical properties

Power Reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

1 IntroductionMichelson-Sagnac interferometer(1)

9

Membrane

From laser source

Beamsplitter

Steering mirror

Steering mirror

1 Introduction　 Michelson-Sagnac interferometer(2)

10

Sagnac mode

Michelson mode

Anti symmetric port (no light of Sagnac mode)

Symmetric port

Membrane position is adjusted to keep this port dark

11

1 Introduction Michelson-Sagnac interferometer(3)

Steering mirror

Steering mirror

Membrane

Beamsplitter

Laser source

Power recyclingmirror

Signal recycling mirror

Recycling techniques are useful even if the membrane reflectance is low

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

3

CLIO-MQM (Cryogenic Laser Interferometer Observatory-Macroscopic Quantum Measurement)

Workshop

24th and 25th May

Waseda Institute for Advanced Study Tokyo Japan

SL Danilishin ldquoTowards mechanical non-Gaussian

states with optical interferometersrdquo

FY Khalili ldquoUp-converter regime in the membrane

experimentsrdquo

K Yamamoto ldquoNano-gram membrane experiment

at AEIrdquo

Related talks

Contents

1 Introduction

2 Current status

3 Future work

4 Summary

4

1Introduction Interferometric gravitational wave detector

Current First generation (LIGOVIRGOGEOTAMACLIO)

Future Second generation

(GEO-HF Advanced LIGO and VIRGO

LCGT AIGO)

Third generation (Einstein Telescope)

Quantum noise Limit of future interferometer

Shot noise Phase fluctuation

Radiation pressure noise Amplitude fluctuation

5

6

1 IntroductionRadiation pressure noise (1)

httpspacefilesblogspotcom

Photons come at random (amplitude fluctuation) Back action of photon is also at randomrarr Radiation pressure noise

7

shot noise

quantum radiation pressure noise

standard quantum limit

quantum noise with 100x increased laserpower

1 Introduction Standard Quantum Limit

Nobody observed radiation pressure noise

Large radiation pressure noise

High laser power Light mass

~ m12

~ P12

~ P-12

Standard Quantum Limit (SQL) is a fundamental limit for

naively optimized conventional interferometers

8

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

Optical properties

Power Reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

1 IntroductionMichelson-Sagnac interferometer(1)

9

Membrane

From laser source

Beamsplitter

Steering mirror

Steering mirror

1 Introduction　 Michelson-Sagnac interferometer(2)

10

Sagnac mode

Michelson mode

Anti symmetric port (no light of Sagnac mode)

Symmetric port

Membrane position is adjusted to keep this port dark

11

1 Introduction Michelson-Sagnac interferometer(3)

Steering mirror

Steering mirror

Membrane

Beamsplitter

Laser source

Power recyclingmirror

Signal recycling mirror

Recycling techniques are useful even if the membrane reflectance is low

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

Contents

1 Introduction

2 Current status

3 Future work

4 Summary

4

1Introduction Interferometric gravitational wave detector

Current First generation (LIGOVIRGOGEOTAMACLIO)

Future Second generation

(GEO-HF Advanced LIGO and VIRGO

LCGT AIGO)

Third generation (Einstein Telescope)

Quantum noise Limit of future interferometer

Shot noise Phase fluctuation

Radiation pressure noise Amplitude fluctuation

5

6

1 IntroductionRadiation pressure noise (1)

httpspacefilesblogspotcom

Photons come at random (amplitude fluctuation) Back action of photon is also at randomrarr Radiation pressure noise

7

shot noise

quantum radiation pressure noise

standard quantum limit

quantum noise with 100x increased laserpower

1 Introduction Standard Quantum Limit

Nobody observed radiation pressure noise

Large radiation pressure noise

High laser power Light mass

~ m12

~ P12

~ P-12

Standard Quantum Limit (SQL) is a fundamental limit for

naively optimized conventional interferometers

8

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

Optical properties

Power Reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

1 IntroductionMichelson-Sagnac interferometer(1)

9

Membrane

From laser source

Beamsplitter

Steering mirror

Steering mirror

1 Introduction　 Michelson-Sagnac interferometer(2)

10

Sagnac mode

Michelson mode

Anti symmetric port (no light of Sagnac mode)

Symmetric port

Membrane position is adjusted to keep this port dark

11

1 Introduction Michelson-Sagnac interferometer(3)

Steering mirror

Steering mirror

Membrane

Beamsplitter

Laser source

Power recyclingmirror

Signal recycling mirror

Recycling techniques are useful even if the membrane reflectance is low

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

1Introduction Interferometric gravitational wave detector

Current First generation (LIGOVIRGOGEOTAMACLIO)

Future Second generation

(GEO-HF Advanced LIGO and VIRGO

LCGT AIGO)

Third generation (Einstein Telescope)

Quantum noise Limit of future interferometer

Shot noise Phase fluctuation

Radiation pressure noise Amplitude fluctuation

5

6

1 IntroductionRadiation pressure noise (1)

httpspacefilesblogspotcom

Photons come at random (amplitude fluctuation) Back action of photon is also at randomrarr Radiation pressure noise

7

shot noise

quantum radiation pressure noise

standard quantum limit

quantum noise with 100x increased laserpower

1 Introduction Standard Quantum Limit

Nobody observed radiation pressure noise

Large radiation pressure noise

High laser power Light mass

~ m12

~ P12

~ P-12

Standard Quantum Limit (SQL) is a fundamental limit for

naively optimized conventional interferometers

8

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

Optical properties

Power Reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

1 IntroductionMichelson-Sagnac interferometer(1)

9

Membrane

From laser source

Beamsplitter

Steering mirror

Steering mirror

1 Introduction　 Michelson-Sagnac interferometer(2)

10

Sagnac mode

Michelson mode

Anti symmetric port (no light of Sagnac mode)

Symmetric port

Membrane position is adjusted to keep this port dark

11

1 Introduction Michelson-Sagnac interferometer(3)

Steering mirror

Steering mirror

Membrane

Beamsplitter

Laser source

Power recyclingmirror

Signal recycling mirror

Recycling techniques are useful even if the membrane reflectance is low

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

6

1 IntroductionRadiation pressure noise (1)

httpspacefilesblogspotcom

Photons come at random (amplitude fluctuation) Back action of photon is also at randomrarr Radiation pressure noise

7

shot noise

quantum radiation pressure noise

standard quantum limit

quantum noise with 100x increased laserpower

1 Introduction Standard Quantum Limit

Nobody observed radiation pressure noise

Large radiation pressure noise

High laser power Light mass

~ m12

~ P12

~ P-12

Standard Quantum Limit (SQL) is a fundamental limit for

naively optimized conventional interferometers

8

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

Optical properties

Power Reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

1 IntroductionMichelson-Sagnac interferometer(1)

9

Membrane

From laser source

Beamsplitter

Steering mirror

Steering mirror

1 Introduction　 Michelson-Sagnac interferometer(2)

10

Sagnac mode

Michelson mode

Anti symmetric port (no light of Sagnac mode)

Symmetric port

Membrane position is adjusted to keep this port dark

11

1 Introduction Michelson-Sagnac interferometer(3)

Steering mirror

Steering mirror

Membrane

Beamsplitter

Laser source

Power recyclingmirror

Signal recycling mirror

Recycling techniques are useful even if the membrane reflectance is low

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

7

shot noise

quantum radiation pressure noise

standard quantum limit

quantum noise with 100x increased laserpower

1 Introduction Standard Quantum Limit

Nobody observed radiation pressure noise

Large radiation pressure noise

High laser power Light mass

~ m12

~ P12

~ P-12

Standard Quantum Limit (SQL) is a fundamental limit for

naively optimized conventional interferometers

8

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

Optical properties

Power Reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

1 IntroductionMichelson-Sagnac interferometer(1)

9

Membrane

From laser source

Beamsplitter

Steering mirror

Steering mirror

1 Introduction　 Michelson-Sagnac interferometer(2)

10

Sagnac mode

Michelson mode

Anti symmetric port (no light of Sagnac mode)

Symmetric port

Membrane position is adjusted to keep this port dark

11

1 Introduction Michelson-Sagnac interferometer(3)

Steering mirror

Steering mirror

Membrane

Beamsplitter

Laser source

Power recyclingmirror

Signal recycling mirror

Recycling techniques are useful even if the membrane reflectance is low

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

8

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

Optical properties

Power Reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

1 IntroductionMichelson-Sagnac interferometer(1)

9

Membrane

From laser source

Beamsplitter

Steering mirror

Steering mirror

1 Introduction　 Michelson-Sagnac interferometer(2)

10

Sagnac mode

Michelson mode

Anti symmetric port (no light of Sagnac mode)

Symmetric port

Membrane position is adjusted to keep this port dark

11

1 Introduction Michelson-Sagnac interferometer(3)

Steering mirror

Steering mirror

Membrane

Beamsplitter

Laser source

Power recyclingmirror

Signal recycling mirror

Recycling techniques are useful even if the membrane reflectance is low

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

1 IntroductionMichelson-Sagnac interferometer(1)

9

Membrane

From laser source

Beamsplitter

Steering mirror

Steering mirror

1 Introduction　 Michelson-Sagnac interferometer(2)

10

Sagnac mode

Michelson mode

Anti symmetric port (no light of Sagnac mode)

Symmetric port

Membrane position is adjusted to keep this port dark

11

1 Introduction Michelson-Sagnac interferometer(3)

Steering mirror

Steering mirror

Membrane

Beamsplitter

Laser source

Power recyclingmirror

Signal recycling mirror

Recycling techniques are useful even if the membrane reflectance is low

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

1 Introduction　 Michelson-Sagnac interferometer(2)

10

Sagnac mode

Michelson mode

Anti symmetric port (no light of Sagnac mode)

Symmetric port

Membrane position is adjusted to keep this port dark

11

1 Introduction Michelson-Sagnac interferometer(3)

Steering mirror

Steering mirror

Membrane

Beamsplitter

Laser source

Power recyclingmirror

Signal recycling mirror

Recycling techniques are useful even if the membrane reflectance is low

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

11

1 Introduction Michelson-Sagnac interferometer(3)

Steering mirror

Steering mirror

Membrane

Beamsplitter

Laser source

Power recyclingmirror

Signal recycling mirror

Recycling techniques are useful even if the membrane reflectance is low

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

1 Introduction Goal sensitivity

12

Temperature 1 KQ 107

Effective Mass 125 ngResonance 75 kHzPower at BS 1 WSignal recycling mirror 998 amplitude reflectance

Radiation pressure noise is 2 and 3 times larger than shot noise and thermal noise

K Yamamoto et al Physical Review A 81 (2010) 033849

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

1 Introduction Node of Sagnac mode

Sagnac mode Clockwise and counterclockwise beams

There is interference between them

Standing wave

Nodes and anti nodes

Anti symmetric port is dark

Membrane must be on node or anti-node

We prefer membrane on node because of absorption

13

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

2 Current status Membrane (Si3N4 in frame)

14

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHzQ ~ 13 x 106

Optical properties

Power reflectance ~ 33 Absorption le 150 ppmFlatness 1 nmMicro roughness 02 nmScattering rarr 0

JD Thompson et al Nature 452 (2008) 72-76

about1 mm

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

15

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane (in Michelson-Sagnac interferometer)

Node of Sagnac mode (small absorption)

Anti node (large absorption)

Fitting Second polynomial(Physical mechanism is not clear yet)

First mode

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

16

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Second mode

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

17

2 Current status Membrane (Si3N4 in frame)

Heat absorption in membrane

Fourth mode Temperature gradient

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

2 Current status Michelson-Sagnac interferometer

18

Without power and signal recycling

NdYAG laser EOM

Mode cleaner

Photodetector

Vacuum tank(10-6 mbar)

Photo detector(signal of membrane motion)

Membrane

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

2 Current status Inside vacuum tank

19

Membrane holder

Steering mirror

Steering mirror

Beam splitter

From lasersource

Antisymmeticport

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

20

2 Current status Measured power spectrum

On resonance Thermal noise

Off resonance Intensity noise

510-16 mrtHz

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

21

2 Current status Standard Quantum Limit on resonance

JILANIST group claims that their sensitivity is below Standard Quantum Limit (SQL)

JD Teufel et al Nature Nanotechnology 4 (2009) 820

4810-15 mrtHz

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

22

SQL

G Anetsberger et al Nature Physics 5 (2009) 909

Recent result from same group(arXiv10033752)

5710-16 mrtHz

2 Current status Standard Quantum Limit on resonance

Max-Planck-Institut (MPI) fuer Quantenoptik group also claims that their sensitivity is below Standard Quantum Limit (SQL)

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

23

Standard QuantumLimit (SQL) of NIST and MPI fuer Quantenoptik is constant around the resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their definition of Standard Quantum Limit (SQL)

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

24

They compare off resonance sensitivity with Standard QuantumLimit (SQL) on resonance

Standard QuantumLimit (SQL) depends on (only) mechanical susceptibility

2 Current status Standard Quantum Limit on resonance

What is their difinition of Standard Quantum Limit (SQL)

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

25

Our sensitivity is also below Standard Quantum Limit (SQL) and better or comparable

510-16 mrtHz

2 Current status Standard Quantum Limit on resonance

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

3 Future work(1) Reduction of noise

(to observe off resonance thermal noise)

Laser intensity stabilization (in progress)

(2) Signal recycling

(3) Cryogenic apparatus (about 1K 3He evacuation)

Suspension

26

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

4 SummaryRadiation pressure noise measurement

with extremely light but translucent membrane

New topology Michelson-Sagnac interferometer

Goal sensitivity Nodes of Sagnac mode

Current status of experiment

Incident power dependence of resonant frequency

Operation without power and signal recycling

Current sensitivity (510-16 mrtHz)

Off resonance sensitivity

below Standard Quantum Limit (SQL) on resonance

Future work

Laser intensity stabilization

Cryogenic apparatus and so on 27

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

28

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

29

1 Introduction Radiation pressure noise

Vacuum

Frequency(Hz)

Sen

siti

vity

(r

tHz)

Radiation

pressure noise

Mirrorthermal noise

Advanced LIGO

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

30

1 Introduction Sizes of oscillators

TJ Kippenberg and K J Vahala Science 321 (2008) 1172

Resonant frequency

Effective Mass

Hz

MHz

kg

pg

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

31

Mechanical properties

frame 752 mm2 x 200 micromArea 15 mm x 15 mmThickness 75 nm Effective mass ~ 100 ngResonant frequency ~ 73 kHz

1 Introduction Membrane (Si3N4 in frame)

JD Thompson et al Nature 452 (2008) 72-76

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

32

GEO600 LIGO3 Adv LIGO3

Sakata1 Goszligler2 Corbitt3 Ours4

meff 1 kg 25 kg 10 kg 23 mg 05g 1 g 50 ng

P [kW] 10 10 830 12 0003 20 006

Pm [kWkg] 10 4 83 52103 6 20103 12109

Pm [kWkg] 3 13 29 48000 110 4500 5109

1 N Mavalvala Elba conference (2008)2 CM Mow-Lowry et al Journal of PhysicsCongerence Series 32 362-367 (2006)3 T Corbitt Elba conference (2008)4 JD Thompson et al Nature 452 72-76 (2008)

1 Introduction compare different approaches

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

2 Theoretical outlines

I will explain

Two differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

and goal sensitivity of our interferometer

33

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

2 Theoretical outlines Radiation pressure noise on membrane

34

Membrane

InterferenceInterference

Conclusion Radiation pressure noise is proportional to power reflectance of membraneeven if the membrane is at node of Sagnac mode

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

2 Current status Optical table

35

Laser source

Mode cleaner

Periscope

Vacuum tank

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

36

2 Current status Membrane holder

Stage

PZT with hole

Membrane frame

Membrane

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

3 Current status Michelson-Sagnac interferometer

37

Beam splitter

Membrane holder Steering

mirror

Steering mirror

From lasersource

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

2 Theoretical outlines Standart Quantum Limit (SQL)

SQL of Michelson-Sagnac interferometer (one membrane)

SQL of Fabry-Perot Michelson interferometer (four mirrors)

SQL of simple Michelson interferometer (two mirrors)

H Mechanical responce of one oscillatorOur conjucture SQL depends on number of mirrors (n)

38

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

39

3 Current status Calibration

Calibration (photo detector output vs displacement of membrane) is possible as like simple Michelson interferometer

Membrane displacement [nm]

Ph

oto

det

ecto

r o

utp

ut

po

wer

[a

u] Measured fringe

Fitting value

Measured results agree with fitting

Quater of wavelength

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

3 Current status Resonant frequencies of membrane

40

Fundamental mode (73kHz)

Frequency (kHz)

Am

pli

tud

e (d

B)

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

3 Current status Resonant frequencies of membrane

41

Difference between theory and measurement (~1)

Frequency [kHz]

Dif

fere

nce

bet

wee

n t

heo

ry

and

mea

sure

men

t [k

Hz]

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

75 nm

15 mm

42

bull Thermoelastic dampingrarr Estimation Q ~ 5 x 107

bull Residual gas damping rarr Vacuum (~ 10-6 mbar)

3 Current status Q-values of membrane

bull Recoil loss rarr Estimation Q gt 107

bull Bulk loss rarr Unknownbull Loss on surface rarr Unknown

bull Our measurement Q ~ 13 x106 300 K

bull Measurement of other group Q ~ 1 x107 03 K BM Zwickl et al Applied Physics Letters 92(2008)103125

Time [sec]

Pressure [mbar]Q

MeasurementTheory

10-6

200 microm

75 nm

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

3 Current status Reflectance of membrane

Membrane

as etalon

Po

wer

ref

lect

ivit

y

43

Incident angle [degree]

P-polarized

S-polarized

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

44

vacuum systemto reach lt 10-6 mbar

actual pressurein experiment1510-7 mbar

backing pump pressure10-1 mbar not good enoughto use ducted vacuum

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

45

Q-measurementactual status of the table

laser preparation

membrane

periscopes

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

46

bull many unknown valuesbull had no verification for Harris results

rarr designed very sturdy mount

recent results

it should be sufficient to conserve Q of the small frame to be not limited

we will design a smaller mount for further experiment

recoil lossenergy transfer to membraneholder limits Q

osc

sup

sup

osc1-sup

1-osc

1osc QQQ

recoil

m

m

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

47

Q-measurementactual readout scheme

bull 106 periods per ringdowntime

rarr use lock in amplifier (variable filters)

our lock-in amp is too slow

rarr mixer shifts signal to some kHz

0f periodper energyloss

energy contained totalQ

ringdown time

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

48

Q-measurementactual readout scheme

106 periods per ringdowntime

rarr mix signal down (shift to lower freq)

Lock-in amp is too slow

rarr second mixer for some kHz

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

49

nonlinearity of the oscillationcomparison of our results to Harris`

Harris et al APL 92 (2008)our results

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

50

locking scheme for PR-cavityusing Pound Drever Hall signal

bull michelson acts as mirror

bull membrane-position dependent reflectivity (and phase)

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

51

locking scheme for Michelson interferometerusing Schnupp asymmetry

bull need different armlength

bull IFO reflecting carrierbull IFO partly transmitting sidebands

bull errorsignal in transmission

problems

bull need to preserve contrast

bull small asymmety

bull high modulation frequency

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

52

outlookfurther techniques

bull dual recycling

bull frequency stabilisation

with reference cavity

bull suspended interferometer

to isolate from seismic motion

(like Tokyo- group)

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

53

KryostatReduzierung thermischen Rauschens

Mehrstufiges Konzept (Zwiebelschalenmodell)

rarr Interferometer durch 4He gekuumlhlt

rarr Membran daruumlber hinaus durch 3He gekuumlhlt

Kryostat verursacht bdquoErschuumltterungenldquo

rarr Seismische Entkopplung des Interferometers

Thermisches Rauschen erfordert Kuumlhlung

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

54

Erwartete Empfindlichkeitfuumlr kryogene Temperaturen

rarr Schrotrauschen Faktor 2rarr therm Rauschen Faktor 3

Temperatur 1 KGuumlte 107

Effektive Masse 125 ngLeistung 400 WResonanz 50 kHz(optische Feder)

Weitere Option bull Signal Recycling (nur gegen Schrotrauschen)

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

62

Groszlige Uumlberschriftkleine Uumlberschrift

Text

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

63

2 Theoretical outlines

Three differences from simple Michelson

(1)Radiation pressure noise on membrane

(2)Node of Sagnac mode

(3)Optical spring

63

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

2 Theoretical outlines Optical spring (1)

Optical spring (without cavity) Light acts as spring

Radiation pressure on membrane depends on its position

Radiation pressure changes

resonant frequency of membrane

6464

InterferenceInterference

Membrane

Shift

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

2 Theoretical outlines Optical spring (2)

Phase of Michelson mode Shift

Sign of shift on right side is opposite to that on left side

Phase of Sagnac mode No shift

6565

Left side of membrane

Sagnac

Michelson

Right side of membrane

Shift by membrane

Shift by membrane

Michelson

Sagnac

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

2 Theoretical outlines Optical spring (3)

Interference Constructive (larger power) on right side

Destructive (smaller power) on left side

Radiation pressure on right side becomes larger

(Optical spring effect)

6666

Sagnac

Michelson

Shift by membrane

Shift by membrane

Michelson

Sagnac

Left side of membrane Right side of membrane

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling

2 Theoretical outlines Goal sensitivity

6767

Temperature 1 KQ 107

Effective Mass 125 ngPower at BS 400 WResonance 75 kHz(with optical spring)Resonance 50 kHz(without optical spring)

Shot noise Factor 2Thermal noise Factor 3

Option Signal Recycling 99 power reflectance Power at BS about 1W P

ow

er s

pec

tru

m d

ensi

ty [

mr

tHz]

Frequency[kHz]

Shot noiseQuantum noiseThermal noise

Without signal recycling