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Brazilian Microwave Frequency Standards
Using Cold Atoms
Daniel Varela Magalhães
XI Escola de Verão Jorge André SwiecaÓptica Quântica e Óptica Não Linear
Instituto de Física de São CarlosUniversidade de São Paulo
Av. Trabalhador São-Carlense, 40013560-970, São Carlos-SP, Brazil
Outline
The “second”
Frequency Standards
Ramsey Method
Comparisons and Measurements (Stability and Accuracy)
Cold Atoms
Experiments: Fountain & TAC
Frequency Synthesis and Links
Future Prospects
Swieca 08
The “second”
Need of StandardisationConvention du Mètre (20 may 1875)
Establishment of BIPM (Bureau International des Poids et Mesures)Requirement for the growth of international trade in manufactured
and industrial products
Adoption, in 1960, of the Système International d’Unités (SI)Metric, electric and photometric unitsSeven base units, derived
and supplementary unitsAlmost universally used in science
and technology
Swieca 08
Lenghtm
Masskg
Times
ElectricCurrent
A
c Cs µ0
Temp.K
Lum. Int.cd
Sub. Qt.mole
Force
J N
C
W
V
Ω F ε0
2e/h
h/e2
Swieca 08
The “second”
metre - The metre is the length of the path travelled by light in vacuumduring a time interval of 1/299 792 458 of a second.
kilogram - The kilogram is the unit of mass; it is equal to the massof the international prototype of the kilogram.
second - The second is the duration of 9 192 631 770 periods of the radiationcorresponding to the transition between the two hyperfine levels of the groundstate of the caesium 133 atom.
ampere - The ampere is that constant current which, if maintained in twostraight parallel conductors of infinite length, of negligible circular cross-section,and placed 1 m apart in vacuum, would produce between these conductorsa force equal to 2 x 10–7 newton per metre of length.
kelvin - The kelvin, unit of thermodynamic temperature, is the fraction1/273.16 of the thermodynamic temperature of the triple point of water
mole1.The mole is the amount of substance of a system which containsas many elementary entities as there are atoms in 0.012 kilogram ofcarbon 12.2.When the mole is used, the elementary entities must be specifiedand may be atoms, molecules, ions, electrons, other particles, or specifiedgroups of such particles.
candela - The candela is the luminous intensity, in a given direction,of a source that emits monochromatic radiation of frequency 540 x 1012 hertzand that has a radiant intensity in that direction of 1/683 watt per steradian.
Swieca 08
The “second”
Mean solar day Astronomical data Material properties
NBS (NIST) technical note, december, 1964
Swieca 08
The “second”
“The standard to be employed is the transition between the two hyperfine levels F=4 , mf=0 and F=3, mf =0 of the fundamental state 2S1/2 of the atom of cesium 133 undisturbed by external fields and the value 9 192 631 770 hertz is assigned.”
1964
“La seconde est la durée de 9192631770 périodes de la transition correspondant à la transition entre les deux niveaux hyperfinsde l’état fondamental de l’atome de 133Cs”
1967
Experiments since 1955L. Essen and J. Parry (NPL)
New definition dependingon the reliability od the system
Swieca 08
The “second”
Swieca 08
The “second”
Consequences and uses of such reference
Outstanding frequency referencesStability, accuracy, realiability, ...
Development of National Standards
Research in Fundamental PhysicsAtomic Physics – collisions, freq. shifts, ...Tests of Fundamental ConstantsHigh Resolution Absolute SpectroscopyQuantum InformationCold Atoms in Space (ACES, PARCS)
Traceability of other units to the time unit
second
c
meter
2e/hc,ε0
ohm volt
ampere
Force measurement µ0
kilogram
Swieca 08
The “second”
Frequency Standards
Cold H
Cs, Rb:Laser optical pumping
Cs fountain
Ion trap
Ion laser cooling
CoherentPopulationTrapping
Quantum transitionsQuantum transitions
Optical standardsOptical standards Microwave standardsMicrowave standards
Saturatedabsorption
Saturatedabsorption
Othertechniques
Othertechniques
Cells: CH4, I2, OsO4, CO2, Rb,H2O…
Ramseyfringes
Mono-ion
Two-photon
Neutral Atoms
H, Cs, RbH, Cs, Rb Othertechniques
Othertechniques
Optical comb
Swieca 08
Frequency Standards
)NS(Q)(
a
1∝τσQ is for quality (δf/f )
CPT standardsSmall devices for portable applications
Optical domain standards
Excellent prospects – Future redefinition of the second ???Limits related to long term stab. and SNR (Ions x Neutral Atoms)
Sr x Ca – Uncertainty at 1.5x10-16; Stability at 2x10-15
Hg+ x Al+ - Uncertainty at ~2x10-17; Stability at ~2x10-15
Beam standardsGreat number of laboratory and commercial systems, bigger contributor for TAILimitations related with velocity dispersion and accuracy limits
Atomic fountain standardsBest realization of the secondAccuracy at 4x10-16
Stability at 1.6x10-14 at 1s
Swieca 08
The 133Cs as a primary standard
Passive standard – The atom must be interrogated respect to a local oscillator
Transition frequency in the X band – 9192631770Hz
Methods used for microwave spectroscopy - NMR
9192,6MHz2
126 S F=3
F=4
Swieca 08
Frequency Standards
100MHz 10MHz
9.2GHz
100MHz100MHz 10MHz10MHz
9.2GHz9.2GHz
Passive frequency standard
Search for techniques to better interrogate the atomic transition
Swieca 08
Frequency Standards
LocalOscillator
AtomicDiscriminator
ControlSystem
Ramsey Method
The Rabi methodCs oven and stateselection region
<v>
l
Interaction region: Microwave cavity
State analysis anddetection region
Cesium beam
b
a3
k1
k2
k3
ωRτ
ωµw
A
l
CavityLl
Cesium beam<v>
Cavity
k
2
a3(τ+T+τ)
k
2bk1
a3(0)
k3
ωRτ
ωµwa3(τ)
k3
bk1
ωµ
wωRτ
k1
k3
k2
a3(τ+t)ωhf
The Ramsey’s method ofSeparated Oscillatory Fields
π pulse – Mag. field ( b ) & Int. time (τ )
2 x π/2 pulses
Swieca 08
ν
P
µµµµW
ν
P
Increasing the resolutionof the measurement
NMR Methods
Ramsey Method
Swieca 08
∆ν∆ν∆ν∆ν
-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 800,0
0,5
1,0
Tra
nsiti
on p
roba
bilit
y
Frequency Modulation (Hz)
LT
πυπν ==∆
( ) ( ) ( )2
00
02
2
2
2 sin2
1sin
2
1cos
2
1cos
2
1sin
4
+ΩΩΩΩ−+ΩΩΩ
Ω= φτφτττ TT
bP
22
0b+Ω=Ω
( ) τττ bbP2
1cos
2
1sin4 22
2 =
Ramsey fringe
Ramsey Method
-100 -50 0 50 1000,0
0,2
0,4
0,6
0,8
1,0
ω-ω0(Hz)
P(τ
)
Lrf
Lrf
Lrf
10L
Lrf
Lrf
10L
12Lrf
Swieca 08
•Real gain
•Field homogeneity
•Interference pattern
Comparisons and Measurements (Stability and Accurac y)
Accuracy
Stability
y(t) - Type A uncertainties (statistical)
ε(t) - Type B uncertainties (systematic)
Enviromental effects
Right valueMeasured values
Swieca 08
( ) ( )[ ]tytt ++= )(10 ενν
Tra
nsiti
on p
roba
bilit
y
Modulation (Hz)- ννννm + ννννmνννν0
0
0,5
1,0
Locking the LO to the atomic resonator
Type B uncertainties
Swieca 08
Frequency Shifts
Comparisons and Measurements (Stability and Accurac y)
ν0 ν = ν0 + ε
For atomic references
1. Second order Zeeman effect2. Blackbody radiation3. Colisional effect4. Rabi pulling5. First and second order
Doppler effect6. Cavity pulling7. Light shift8. Microwave leaks
ii σεε ±=Frequency shift
The definition of the second is defined as free of any disturbance
Accuracy budget
( ) 2/1131021 −−×− τ ????τ
(((( ))))tx
(((( ))))ty
τ
(((( ))))tx
(((( ))))ty
Oscillatorunder test
ReferenceOscillator
f / N TimeIntervalCounter
Data rec.f / N
St
Sp
(((( ))))0
01
y
yyty
−−−−====Fractional Frequency
Swieca 08
Comparisons and Measurements (Stability and Accurac y)
( ) ( ) ( )( )2
1
2
2
1tytyy −+= ττσ ( ) ( ) ( )
21
1
1
2112
1
−−
≅ ∑−
=+
M
iiiy yy
Mτσ
( ) ( ) ( )2
12
1
2122
222
1
+−
−≅ ∑
−
=++
N
iiiiy xxx
N ττσ
Finite data
Phase difference data – 1 PPS
Problems with simple variance calculations
Allan variance
Swieca 08
Comparisons and Measurements (Stability and Accurac y)
5 MHz
SR620
Counter
GPSAgilent
GPIB
Counter limitations < 10-11
Comparisons and Measurements (Stability and Accurac y)
Swieca 08
Phase comparisons – Improving performance
LPF
Voltmeter
Comparisons and Measurements (Stability and Accurac y)
Padrão de
Referência
PLL
Síntese de
Microondas
10MHz 10MHz
VCO 10MHz
DS345
DAQ
GPIB
Tempo
Variância de Allan
III
III
Mod
9192631770Hz
( )0
01
ννν −=ty
Padrão de
Referência
PLL
Síntese de
Microondas
10MHz 10MHz
VCO 10MHz
DS345DS345
DAQDAQ
GPIBGPIB
Tempo
Variância de Allan
III
III
Variância de Allan
III
III
Mod
9192631770Hz
( )0
01
ννν −=ty
Comparisons and Measurements (Stability and Accurac y)
Atomic Standards
Why Cold Atoms?
9,192GHz
9192,6MHz2
126 S F=3
F=4
Swieca 08
Why Cold Atoms?
T = 363 KT = 293 K
ττττ
f(ττ ττ)
Swieca 08
Why Cold Atoms?
T = 363 KT = 293 K
ττττ
f(ττ ττ )
Swieca 08
Cold Atoms
H1 = 2.5 mH2 = 5.9 m
Zacharias’ Fountain – Mid 1950’s
Swieca 08
Cold Atoms
First Laser-Cooled Fountain
~ 4 Hz Fringe
Swieca 08
Cold Atoms
Ramsey resonance in a Zacharias fountainA. Clairon, C. Salomon, S. Guellati, W. D. PhillipsEurophys. Lett., 16(2), pp.165-170 (1991)
A Cesium Fountain Frequency Standard:PreliminaryResults
A.Clairon, Ph. Laurent, G. Santarelli, S.N. Lea, S. Ghezali, M. Bahoura
CPEM 1994 Conference Digest, pg. 149
Laboratory Experiments Operational Frequency Standards
1991-1995
Swieca 08
Experiments – Atomic Fountain
Swieca 08
Magneto-optical trap
Six counterpropagating beams – 3 axisAnti-Helmholtz coils108 – 109 Cs atoms in 1-2s
10-20A
MOT
Experiments – Atomic Fountain
Swieca 08
Optical molasses
Six counterpropagating beams – 3 axisAnti-Helmholtz coils offSub-Doppler temperaturesHomogeneity of the atomic cloud100-300ms
MOT mol
Experiments – Atomic Fountain
Swieca 08
Launch of the parabolic flight
Upper beam red tuned, down beamsblue tuned
Initial velocity determined by the detuning1-3ms
MOT mol Launch
Experiments – Atomic Fountain
Swieca 08
Sub-Doppler cooling
Fast detuning and attenuation of thebeams
The atoms are still in the beams zoneThe Cs cloud reach temp. below 10µK1-4ms
MOT mol Launch
S-Dcooling
Experiments – Atomic Fountain
Swieca 08
Selection I – mf = 0
Rabi pulse in the first µwave cavityTransference of the atoms at mf = 0
µµµµW
MOT mol Launch
S-Dcooling
Sel
I
Experiments – Atomic Fountain
Swieca 08
Selection II – mf = 0
Light pulse tuned to push the atoms at mf ≠ 0Transference of the atoms at mf = 0
MOT mol Launch
S-Dcooling
Sel
III
Experiments – Atomic Fountain
Swieca 08
Interrogation I
First pass of the atoms in the µWave cavityPower control to apply a π/2 pulse µµµµW
MOT mol Launch
S-Dcooling
Sel
II
Int
I I
Experiments – Atomic Fountain
Swieca 08
Interrogation II
Dark flight of the cloudDefines the linewidth of the observed transition
MOT mol Launch
S-Dcooling
Sel
II
Int
I III
Experiments – Atomic Fountain
Swieca 08
Interrogation III
Second pass of the atoms in the µWave cavityPower control to apply a π/2 pulse µµµµW
MOT mol Launch
S-Dcooling
Sel
II
Int
I III III
Experiments – Atomic Fountain
Swieca 08
Detection
MOT mol Launch
S-Dcooling
Sel
II
Int
Fluorescence of the cloudDiferential method to minimize fluctuationsEvaluation of Nat in each hyperf. level and T
I III IIIDet
Experiments – Atomic Fountain
Load and launch 107 -109 Cs atoms in 300-1500 ms. Atoms are all in | F= 4, mF > - MOT,molasses,2D-MOT. State Selection π-pulse moves atoms in
| F = 4, mF =0> → | F = 3, mF = 0>. Optical pulse removes remaining | F = 4, mF ≠0>
atoms, leaving a pure | F = 3, mF = 0> sample. Ramsey spectroscopy atoms. (on way UP
and way DOWN.) Detection region measures populations in
| F = 4, mF =0> and | F = 3, mF = 0>.
251MHz201MHz151MHz
D2
852.
1 nm
23
26 P
9192.6MHz2
126 S F=3
F=4
F’=4F’=3F’=2
F’=5
T &
CR
ep
Swieca 08
Experiments – Atomic Fountain
Swieca 08
Vacuum system
Optical system
Diode lasers
AOM’s
Fluorescence detection
Trapping and cooling
Interrogation of the atomic transition
Interrogation signal generation
PLL techniques
Control of the 9.192GHz signal
Experiment Control
Temporal sequence
Signal Acquisition
Data storage
The Laboratory Setup
Experiments – Atomic Fountain
Swieca 08
~109 Cs trapped atoms
0,5 1,0 1,5 2,0 2,5 3,020
40
60
80
100
120
Tem
pera
ture
(10
-6K
)
Detuning (Γ)
0,5 1,0 1,5 2,0 2,5 3,0
0,0
0,2
0,4
0,6
0,8
1,0
Nor
mal
ized
cap
ture
effi
cien
cy
Detuning (Γ)
Experiments – Atomic Fountain
Swieca 08
Loading the sample to be interrogatedMOT – molasses transference
1 2 3 4 5 6 7 810
15
20
25
30
35
40
45
Tem
pera
ture
(10
-6K
)
Detuning (Γ)
1 2 3 4 5 6 7 8
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
Num
ber
of a
tom
s in
the
TO
F s
igna
l (no
rm)
Detuning (Γ)
MOT molasses
Some limits in the trap laser
Experiments – Atomic Fountain
E1E2E1E2
80MHz80MHz
80MHz80MHz
DS345DS345
∫∫
∫∫
Escravo
Mestre
TravaFreqüênciaou Fase
Slave
Master
Freq. orPhase lock
Swieca 08
Launching Cold Atoms in a Moving Molasses
laserlaserlaunch v∆= ..3λυ
0,0 0,3 0,6 0,9
0
1
2
3
0,4 0,5 0,6 0,7 0,8 0,9-0,02
0,00
0,02
0,04
0,06
0,08
0,10
0,12
0,14
Inte
nsid
ade
/ V
Tempo / s
19,45 cm after the 2nd cavity5,6 MHz
Flu
or. s
igna
l (V
)
Time (s)
Free fall
InterrogationCavity
SelectionCavity
Cutoff waveguide1 cm
Modo TE 102
4,65 cm
2,286 cm
10 cm
QR = 8358
QP = 1128 1,5 cm
Free flightTube
InterrogationCavity
SelectionCavity
10 c
m
1 cm
a
d
Antinode∆∆∆∆F = ±1 e ∆∆∆∆mF = 0
Copper cavity – Qld > 5000
Mode TE011 – constant phase to avoid first order Doppler
Swieca 08
Experiments – Atomic Fountain
10MHz2f f/10 2f
100MHz
SamplingMixer
4.6GHz
DS345
Isol.~~/ out
in
out
in
out
2f
2f
out
out
in
∫
Maser
HP
OtherChain
ORD
in PC
~~/~/
f/8
3.6MHz
~29MHz
out
∫+offset
∫
∫
∫
High performance oscillators Phase locked loops
Swieca 08
Experiments – Atomic Fountain
1 10 100 1000 10000 100000-160
-140
-120
-100
-80
-60
ORD de 9,192GHz
VCXO de 100MHz
BVA de 10MHz
Sφ,
dB
(rad
2 /Hz)
@10
0MH
z
Freqüência (Hz)
1 10 100 1000 10000 100000-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
Sφ, d
B(r
ad2 /H
z)
@ 9
.192
GH
z
frequency, Hz
Cadeia de Interrogação X Cadeia de Preparação
Pharao X Cadeia de Interrogação
10 1001E-14
1E-13
σσ σσ y(s-1)
ττττ (s)
Oscillators phase noise
Phase noise of the output signalSwieca 08
Use the best spectral partof each oscillator
Experiments – Atomic Fountain
Swieca 08
Experiments – Atomic Fountain
Time of Flight Detection
f = 53 mm f = 20 mm
Photodetector
Atomic cloud
Detection BeamF = 4 ↔↔↔↔ F´ = 5
RepumpF = 3 ↔↔↔↔ F´ = 4
Optical Fiber
Polarizing Cube
Detection Laser
Repump Laser
Differential method to minimizefluctuations
Swieca 08
Experiments – Atomic Fountain
0,0 0,1
0
2
4
Flu
ores
cenc
e S
igna
l (V
)
tof (s)
Cross Talk
0,04 0,06 0,08
0
6
12
Flu
ore
sce
nce
Sig
na
l (V
)
tof (s)
Cross Talk
34
4
==
=
+=
FF
F
NN
NP
TransitionProbability
Detection F=3+4
Detection F=4
Reduction of Crosstalk effectsCollection OpticsAlignement
Time of Flight Detection
-40 -20 0 20 400
2
4
6
8
10
Tra
nsiti
on P
roba
bilit
y (a
.u.)
Frequency Detuning (Hz)
Swieca 08
Experiments – Atomic Fountain
Ramsey Fringesmf = 0
10 1001E-13
1E-12
Squ
are
Roo
t of A
llan
Var
ianc
e (σ
(τ))
Integration Time ( ττττ ) (s)
Tc = 5.2s and Q at = 6.56 x 109
( ) 21121018.5 −−×= ττσ y
-600 -400 -200 0 200 400 600
0
1
2
3
4
5
6
7
8
Tra
nsiti
on P
roba
bilit
y (%
)
Frequency detuning (Hz)
Swieca 08
Experiments – Atomic Fountain
-2,636 x 10-5-2,05 x 10-2Blackbody radiation
0,412,972nd order Zeeman effect
____-2,08 x 10-32nd order Doppler effect
-1,0 x 10-3-1,0 x 10-2Gravitational effect
Uncertainty x 10-12
Shift x 10-12
Effect
Preliminar accuracy budget
1. Colisional effect2. Rabi pulling3. Cavity pulling4. Light shift5. Microwave leaks
Direct probing of cold atoms – no launching
Experiments – TAC
First tests in using an antenna
Direct probing of cold atoms – no launching
-200 0 200 400
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
Model: Lorentz Equation: y = y0 + (2*A/PI)*(w/(4*(x-xc)^2 + w^2))
y0 0.1038 ±0.01651xc 83.2253 ±1.46544w 39.31663 ±5.65373A 61.05288 ±6.29037
Flu
ores
cênc
ia (
U.A
.)
ν − νο (Hz)
Rabi 12 ms (atenuação 0.5) Ajuste lorentziano
( ) 2/111y 104.9 −−×= ττσ
Experiments – TAC
Rabi interrogation39Hz linewidth
-400 -200 0 200 400
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
Experimental Simulation
Flu
ores
cenc
e (a
rb. u
nit)
Frequency (Hz)
-600 -400 -200 0 200 400 600-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1 Experimental Fringes Simulation
Pro
babi
lity
Frequency (Hz)
Problems with the Ramsey methodPoor contrast observed
Experiments – TAC
Model based on the phase differencebetween the two pulses, dueto the cloud expansion
Experiments – TAC
TAC upgrade
New optical systemMicrowave cavity sculpted in the vacuum chamber
Vacuum chamber in SS-316L
Swieca 08
Frequency Synthesis and links
H - MaserCH1 - KVARZ
Commercial Standards – 5071A
Atomic FountainTime transfer
Other standards or Evaluation Systems
Time transfer – Remote comparisons
Traceability to BIPMCircular T
T T1 T2
One way transfer Two way transfer
Common viewcomparison
Swieca 08
54290 54300 54310 54320 543303876508000
3876508500
3876509000
3876509500
3876510000
3876510500
with frequency offset correction
5071
A-G
PS
(0.
1ns
)
MJD
without frequency offset correction
Swieca 08
Frequency Synthesis and links – Local Standards
54389 54390 54391 54392 54393 54394 54395 54396
9098592600
9098592800
9098593000
9098593200
9098593400
9098593600
9098593800
9098594000
9098594200
Mas
er-G
PS
(0.
1ns
)
MJD
without frequency offset correction
with frequencyoffset correction
GPS comparisons
Calibration of local standards – Long termTraceability to BIPM - TAI
Cs – 5071A – High perf. tube H Maser – CH1
Swieca 08
Frequency Synthesis and links – Local Standards
Allan VarianceDetermination of sample size – Counter limitLong term comparisons
Cs X Maser GPS X Maser
Future Prospects
•Characterization of Current Experiments
•Collisions in a Fountain Clock
•Different Frequencies to Squeeze the Ramsey Fringe
•Magic Wavelength for Cs, Rb
•Remote Comparisons of Current Experiments (ONRJ, LNE-SYRTE)
•Fountain Contribution to TAI
•Absolute Spectroscopy
•Optical Clocks – (LNE-SYRTE Hg Clock)
•New Generation of Microwave LO – Optical to µW sense (LNE-SYRTE OPUS)
The Team
Diego Lencione Renato F. Alves
Aida Bebeachibuli