Exploration of the Ultracold World

Ying-Cheng Chen(陳應誠 ), Institute of Atomic & Molecular Sciences, Academia Sinica

12 October, 2009, NDHUIAMS

Outline• Overview of Ultracold Atoms• Introduction to Ultracold Molecules• Exploration I: Molecular cooling• Exploration II: Nonlinear optics with ultraco

ld atoms

Studying, Research and Life: Adventure & Exploration

Temperature Landmark

106 103 1 10-3 10-6 10-9

0

(K)

Core of sun

surface of sun

Room temperature

L N2

L He3He superfluidity

2003 MIT Na BEC

Typical TC

of BECRb MOT

Sub-Doppler cooling

What is special in the ultracold world?

• A bizarre zoo where Quantum Mechanics governs– Wave nature of matter, interference, tunneling, resonance

– Quantum statistics– Uncertainty principle, zero-point energy– System must be in an ordered state – Quantum phase transition

Tmkh B 2 ~1μm for Na @ 100nk

Matter wave interference, MIT Fermi pressure, Rice Vortex Lattice, JILA &MITSuperfluid-Mott insulator tRansition, Max-Planck

Laser Cooling & Trapping

• Cooling, velocity-dependent force: Doppler effect• Trapping, position-dependent force: Zeeman effect

Laser

fv

Atom

v

Magnetic Trapping & Evaporative Cooling

)()( rBrU

Microwave transition

Modern Atomic Physics : Science & Technology

Precision measurementAtomic clock

Test of particle physics (EDM)Test of nuclear physics (parity violation)

Test of general relativityVariation of physical constants

Quantum information scienceQuantum control

Quantum teleportationQuantum network

Quantum cryptographyQuantum computing

Quantum simulation of condensed-matter physics

BEC/Degenerate Fermi gasSuperfluidity/superconductivity

Quantum phase transitionBEC/BCS crossoverAntiferromagnetism/

high Tc superconductivity

Opto-mechanics& Nano-photonicsLaser cooling of mirror/mechanical oscillator

Coupling of cold atom with mesoscopic(nano) objectQuantum limit of detection

Near field optics

Extreme nonlinear opticsAtom/molecule under intense short pulse

High harmonic generationX-ray laser

Attosecond laser

Atom manipulation

Core technology

Laser advancement

Weakness:Molecule manipulation

Double Helix of Science & Technology

Science

Technology Better understanding of science helps technology moving forward

Better technology helps to explore new science

It is a tradition in AMO physics to extend new technology to explore physics at new regime.

Core Technology• Atom cooling

• Laser technology

LasersUltra-intense

Ultra-short

Ultra-stable

Ultra-narrow-linewidth

Non-classical (single photon,

entangled photon pairs)

Laser cooling

100TW

Sub-Hz

250 as

Sub-Hz

atom trapping/optical lattice evaporative cooling

)()( rBrU

Microwave transition

Magnetic-tuned Feshbach resonance

Cold Molecules: Why ?• Test of fundamental Physics.

– Search for electron dipole moment…

• Quantum Dipolar Gases– Add new possibility in quantum

simulation. • Cold Chemistry

– Chemistry with clear appearance of quantum effects

– Controlled reaction• Quantum Computation

– Long coherence time and short gate operation time

TSd

P +-

-+ +

-

rr tt

Cold molecules : How ?

Buffer gas cooling

Electric,magnetic,

optical deceleration

Enhanced PA?Laser cooling?

Sympathetic cooling?Evaporative cooling?

Photo-association

Coherent transfer from Feshbach

molecule

Direct approach

Indirect approach ＋

Breakthrough in Indirect Approach• The door to study quantum degenerate dipolar gases and quantum information with pola

r molecules is opened by JILA’s recent experiment with indirect approach.

K.-K. Ni et alScience, 18,1(2008)

Laser Cooling of Molecule ?Not so cool !

• Its impractical to implement laser cooling in molecules due to the lack of closed transition with their complicated internal structures.

See, however, Di Rosa, Eur.Phys. J. D31,395 (2004) for molecules with nearlyclosed transition.

The ying and yang (dark/bright) sides of molecules. You have to pay the price !

Our approach ? General considerations

• Choose the direct approach to make cold molecules in order to have more impacts in other fields as well.

• Generate a large number of molecules in the first stage.• Build an AC trap in order to avoid the inelastic collision loss. • Use sympathetic cooling with laser-cooled atoms in the ac trap to ov

ercome mK barrier for direct cooling.• What advantages to take? What disadvantages to live with?

Moleculesprecooling

loadingTrapping

Laser-cooledatoms

loading

sympathetic coolingInelastic collision?Reaction?

Ultracold Molecules

Routes Towards Ultracold Molecules

Buffer gas cooling plus magnetic guiding

Sympathetic cooling in a microwave trap by ultracold cesium atoms.

1 K 1 mK 1 μK

Evaporative cooling in a microwave trap.

hotter molecules

colder molecules

Cs atom

SrF molecule

Radiative damping& trap loading

Recent Ideas

Buffer gas cooling plus magnetic guiding

Direct laser cooling

1 K 1 mK 1 μK

Evaporative cooling in an optical dipole trap.

hotter molecules

colder molecules

A2Π1/2

X2Σ1/2

v’’

012

v’0

ω00

A00A01 A02

4

00

02

2

00

01

10

10

AAAA

What molecule? SrF, Why? • Alkali-like electronic structure with strong transitions at visible wavel

engths. Easy to be detected by convenient diode lasers.• Large electric dipole moment, 3.47 D and many bosonic and fermio

nic isotopes . More possibilities in the future.• Microwave trapping consideration. Available microwave high power

amplifier at its rotational transition (2B~ 15 GHz). • With nearly diagonal Frank-Condon array that allow direct laser cool

ing with reasonable number of lasers. • Suitable for test of fundamental physics and quantum information sc

ience.• Radical molecules. Disadvantages in molecule generation.• What advantages to take? What disadvantages to live with ?

Buffer Gas Cooling

P11(8.5)

P11(7.5)

P11(6.5)P11(5.5)

Q12(7.5)

Q12(6.5)

Q12(5.5)

Q12(4.5)

X2Σ,v=1→A2Π1/2,v’=1

SrF molecules generated by laser ablation of SrF2 solid.

Development of an intense SrF Molecular Beam

2B+3 SrF2(high-temperature~1500K)→BF3+Sr+2SrF+BF

SrF+Sr+

BF+2(neutral BF3)

BF+

N+2 CO+

2

RGA Trace

If one want to work with (cold) molecules then he need to learn some chemistry !

Electron-bombardment heating

SrF Beam Characterization

Brewster window

Light baffle

Residual gas analyzer

Turbo pump

skimmer

Laser beam

PMT

ψ3mm ψ2mm

5cm 13cm 10cm

chopper

oven

ECDL laserNew Focus 6009/6300 Toptica WS-7

Wavelength meter

Setup for laser-induced fluorescence

Even near the congested band edge, all hyperfine lines are well resolved !

Typical Spectrum

(0,0) vibrational band ofA2Π1/2- X2Σ+ transitionof 88SrF

Laser intensity ~5 00mW/cm2

FWHM linewidth ~ 130MHzS/N ratio >200

Laser intensity ~ 5mW/cm2

FWHM linewidth ~ 15 MHzS/N ratio > 50Hyperfine lines resolved (I=1/2 for 19F)

Beam CharacterizationFlux v.s. oven temperature

Flux stability ~ 20% / one hour

Highest flux of 2.1×1015 /(steradian． sec)! Even stronger and more stable beam is possible by resistive heatingand is under development!“An intense SrF radical beam for molecule cooling experiment” submitted to Phys. Rev. A.

Better Spectroscopy of SrF

The rotational/hyperfine lines of (0,0) A2Π1/2- X2Σ+ band 88SrF have been recorded to 10-4 cm-1 precision with a fitting accuracy of ±10-3 cm-1 to the effective Hamiltonian.

Theoretical Modeling• Effective Molecular Hamiltonian

• Better molecular constants have been determined !

],)[2(41],[

41

)(21))(2(

21

)(;],[2

)(;

22222222

222222

2242

NSJeSJeqpNeJeJq

eJeJqSJeSJeqpH

SLNASALHSNNSNHNDNBH

HHHHH

iiDD

iiD

iiiidoublinglambda

zzdzzorbitspinD

rotspinrot

doublinglamdaorbitspinrotspinrot

parameter T00 B D A p q

Value(cm-1) 15216.33978(19) 0.2528325(12) 2.5274(28)x10-7 281.46333(34) -0.13353(9) 9.32(3.8)x10-5

“High-resolution laser spectroscopy of the (0,0) band of A2Π1/2- X2Σ+ transition of 88SrF ”submitted to J. of Mol. Spec.

Buffer-Gas-Cooled Molecular Beam & Guiding

• On-going work

oven

Dewar

cryostat

Magnetic guide

UHV ChamberSpectroscopyor laser cooling

Helium

SrF

Estimation of Flux (6.6×1015/s) × (9×10-4)x(2.9×10-3)=1.7×1010/s @ ~5K

Already very intense for a radical beam! Higher flux is possible with modified oven.

Turbo pump

Routes Towards Ultracold Molecules

Buffer gas cooling plus ac electric guiding

Sympathetic cooling in a microwave trap by ultracold cesium atoms.

1 K 1 mK 1 μK

Evaporative cooling in a microwave trap.

hotter molecules

colder molecules

Cs atom

SrF molecule

Radiative damping& trap loading

Development of the Microwave Trap

Rotational transition

Red-detunedmicrowave

AC Stark shift

J=0

J=1

Trapping state

Advantages of microwave trap 1. High trap depth ( ~ 1K)2. Large trap volume (~ 1cm3)3. Good optical access. Allow overlap of MOT with trap for sympathetic coo

ling.4. It can trap molecules in the absolute ground states and thus immune to i

nelastic collisions loss at low enough temperature.

U(x)

x

DeMille, Eur.Phys.J D 31,375(2004)

Observation of standing wave pattern by thermal-sensitive LCD sheet

DDRDzPQE in

)2(4 0

0

Q=11000η=0.87Pin=1060WR=0.217mD=0.2m

E0=0.45 MV/m

Trap depth ~ 0.1 Kfor SrF ground state

“ A high-power microwave Fabry-Perot resonator for molecule trapping experiment”Rev. Sci. Inst. In preparation.

Routes Towards Ultracold Molecules

Buffer gas cooling plus ac electric guiding

Sympathetic cooling in a microwave trap by ultracold cesium atoms.

1 K 1 mK 1 μK

Evaporative cooling in a microwave trap.

hotter molecules

colder molecules

Cs atom

SrF molecule

Radiative damping& trap loading

Sympathetic Cooling of Molecules by Ultracold Atoms

• Conceptually easy but depends on unknown collision properties.

time

T M( t

)

Tm

Ta

Teq

Tempature

τth

• Equilibrium temperature

• Thermalization time

• Collision rate

c: a geometry factor and

ma

mmaaeq NN

TNTN

T

)(23

ma

math NN

NN

2)(2 mama MMMM

),( maampmpa TTcvnn

Larger number of cold atoms,colder atom temperatureand higher atom densityimplieslower molecular temperatureand shorter thermalization time.

Large-number Ultracold Atom System

• Initially developed for molecule sympathetic cooling (with N~ 1010).• Found its application in low-light-level nonlinear optics based on

electromagnetic-induced transparency (EIT).

“An elongated MOT with high optical density”Optics Express 16,3754(2008)

7cm

Absorption Spectrum

Optical density=105for Cs D2 line F=4 →F’=5

trapping beam

trapping

Coils&cell

trapping

Atom cloud probe

Quest of Second Stage Cooling to overcome the mK Barrier for Direct Approach

• Sympathetic cooling with ultracold atoms– Not so promising due to strong in

elastic loss– AC trap is necessary

• Cavity laser cooling– Haven’t been demonstrated.

• Direct laser cooling – Being demonstrated– Limited to a few species

• Single-photon (information) cooling– In combination with magnetic tra

pping– May be demonstrated soon

• ...

A2Π1/2

X2Σ1/2

v’’

012

v’0

ω00

A00A01A02

4

00

02

2

00

01

10

10

AAAA

M.Raizen

pp ,

N

Scattering rate

acp

atomic linewidthΓ

cavity linewidthκ

cavity-enhanced Rayleigh scattering

Laser Cooling of SrF : to overcome the mK barrier!

• Di Rosa, Eur.Phys. J. D, 31,395 (2004)

state X2Σ,v=0 v=1 v=2 v=3

A2Π, v=0 0.9895 0.0103 1.33x10-4 1.57x10-6

A2Π1/2

X2Σ1/2

v’’

012

v’0

ω00

A00

A01A02

4

00

02

2

00

01

10

10

AAAA

J Phy Chem A, 102,9482,1998

0.9998673600=62%

KTkvm 1,3600~

By repumping the v=1 population back to v=0, the transition is closed to 10-4 level

A2Π1/2,v’=0

X2Σ1/2(v’’=0)663.1nm

X2Σ1/2(v’’=1)685.1nm

N’’

0

1

2

J’

J’’

parity

parity

2.5

1.5

0.5

2.51.51.50.50.5

＋－＋

＋－

－－－

＋＋＋

main repumpingnearestinterference

(0,0

)Q11

(0.5

)

(0,0

)P12

(1.5

)

(0,1

)Q11

(0.5

)

(0,1

)P12

(1.5

)

(0,0

)R12

(1.5

)

(0,0

)Q12

(1.5

)

Nearest>14GHz away

~45GHz

A2Π1/2,v’=0

X2Σ1/2(v’’=0)663.1nm

N’’

0

2

J’

J’’

parity

parity

0.5

1.5 ＋＋

－

(0,0

)Q11

(0.5

)

(0,0

)P12

(1.5

)

0.5

F’’

1

0

26.79MHz80.38MHz

112.19MHz

1

2

N’

0

21.75MHz29.72MHz

F’1

0Small ~ few MHz

Considering to rotational states, four lasers (two @ 663nm and two @685nm ) required to close the transition to 10-4 level.

Considering to hyperfine states, it is necessary to generate two frequencies differed by ~50 or 107 MHz by acousto-optical modulator for each laser.

Nonlinear optics with ultracold atoms

- Detour of my planned journey but back to my old track !

Electromagnetically-induced Transparency

Coupling laser

Probe laser

Transparent!

0,5.0,0 3 cc

|1>

|3>

p32

2>

c32

probe coupling

＝ ＋ ＋ ＋…

Path i Path iiiPath ii

2totA

|1>

|2>

|3>

Physical origin: destruction interference between different transition pathways!

EIT, Propagation Effect

00 |)/(

|

p

pppp

pg ddnn

cdkd

v

• Large optical density and small ground-state decoherence rate are two crucial factors in EIT-based application, e.g. optical delay line.

)()()

23()11(

312

31

312

312

cc

g

gd ODLN

cLn

cvL

Slow light !

Vg<17m/s, Hau et.al. Nature397,594,1999

Nonlinear Optics with Ultracold Atoms• With on-resonance signal, one can control the

absorption/transmission of probe photon by signal photon. Photon switching.• With off-resonant signal, one can control the phase of probe photon

by signal photon. Cross phase modulation.

3

21

4

couplingprobe signal

Without signal

With signal beam

Schmidt & Imamoglu Opt. Lett. 21,1936,1996

γ

XPM Application: Controlled-NOT gate for Quantum Computation

• CNOT and single qubit gates can be used to implement an arbitrary unitary operation on n qubits and therefore are universal for quantum computation.

• Single photon XPM can be used to implement the quantum phase gate and CNOT gate

For a good introductory article, see 陳易馨 & 余怡德 CPS Physics Bimonthly, 524, Oct. 2008

Truth table for CNOT gateTCTCTCTC

TCTCTCTC

0111;1101

1010;0000

Signal

Probe

PBS PBS

Atoms

Control qubit

Target qubit

1

0

10 or

Reduction of Ground-state decoherence rate

Coupling ECDL

VCSEL

ProbeDL

λ/2PBS

frequency

coupling

VCSELprobe

~9GHz

Bias-TeeIdc

RF

Reduction of mutual laser linewidth

~10Hz

Beatnote between coupling & probe laser

Reduction of inhomogeneity of straymagnetic field

Faraday rotationas diagnosis tool.Three pairs of coilsfor compensation.

350kHz/Gauss for Cs

BL

FFT

δB<2mG limited by 60Hz AC magnetic field!

Without compensation

With compensation

Good EIT SpectrumObtained EIT with ~50% transmission at 200kHz width for OD~ 60 for Cs D2 F=3 →F’=3 transition.

The Slow Light

10μs for ~2cmatomic sample !Vg~2000m/s

XPM with Group-Velocity-Matched Double Slow Light Pulses

• Both probe & signal pulses becoming group-velocity-match slow light in a high OD gas for longer interaction time. M. Lukin Phys. Rev. Lett. 84, 1419 (2000).

3

2

4

couplingprobe signal

1

signal

Atom A

Atom B

medium

probe

signal

Double EIT Spectrum

• Photon-switching with on-resonance signal field has been observed. • XPM work is underway !

mF= 0 1 2 3 4

F=4, gF=4/15

F=3, gF=0

F=4, gF=1/4

F=3, gF=-1/4

C1

P1

C2 P2P2

P1

(a)

Cs 6S1/2 -6P3/2 (D2-line)

Matching the Group Velocity

Td(P1)

Td(P2)

Group velocity matched !

Probe 1 Probe 2

No atoms

IC1

fixed

decreaseIC2

Future Work : Cavity Enhanced Cross Phase Modulation

• A “holy grail” in nonlinear optics is to realize a mutual phase shift of πradian with two light pulses containing a single photon.

• It can be applied to the implement of controlled-NOT gate for quantum computation and to generate quantum entangled state.

• Few-photon-level XPM is challenging ! – Large Kerr Nonlinearity– Low loss– Strong focusing to increase the atom-laser intera

ction strength– Long atom-laser interaction time

• We are working on cavity-enhanced XPM. The technology may also be applied to cavity laser cooling of molecules in the future.

cold atom

Signal beam

Coupling&probe

The Setup

Acknowledgement• Financial support from NSC, IAMS.• Helps from many colleagues, WY Cheng, KJ Song, J Lin, K Liu, SY Chen…

• Current member: – Chih-Chiang Hsieh – Ming-Feng Tu– Jia-Jung Ho– Wen-Chung Wang

• Former member– S. -R. Pan (now in Colorado state University)– H.-S. Ku (now in Univ. of Colorado/JILA)– T.-S. Ku (now in Univ. of Colorado/JILA)– Prashant Dwivedi (now in Germany’s Univ.)– P.- H. Sun (now in industry)

Keep walking !Molecule cooling

Nonlinear optics with ultrcold atomsWelcome to join us !

Ultracold Atom and Molecule Lab IAMS, Academia Sinica

Slow Light : Dark-State Polariton

2

2

21

cos

0),(]cos[

;tan

),(sin),(cos),(

cv

tzz

ct

kkkn

etzNtzEtz

g

pcg

kzip

coupling

1>

|2>

|3>

coupling

1>

|2>

|3>

probecoupling

1>

|2>

|3>

probe

Lukin&Fleischhauer, PRL 84,5094,2000

Light component

Matter component: atomic spin coherence

EIT and the Photon Storage• By adiabatically turn off the coupling light, the probe pulse can completely

transfer to atomic spin coherence and stored in the medium and can be retrieved back to light pulse later on when adiabatically turn on the coupling.

• This effect can be used as a quantum memory for photons.• The photon storage and retrieved process has been proved to be a phase

coherent process by Yu’s team.

coupling

probe

Hau et.al. Nature, 409,490,2001 Y.F. Chen et.al. PRA 72, 033812, 2005

Q-Value Measurement Under High-Power Operation

0

/)0()(

QeUtU t

microwave OFF

Quality-factor

Coupling efficiency

PLocked

PUnlocked

Unlocked

Locked

PP

1

Cavity Frequency Locking• Pound-Drever-Hall Scheme to obtain error signal• Feedback by vacuum linear translation stage• Locked to better than 50 kHz (linewidth ~ 700kHz)

Locked

Fabry-Perot Cavity Coupling

• Coupling by a circular horn through mirror with mesh.• Obtained optimum coupling through systematic study by varying mesh

parameters.

Reflection signal

Observed Line narrowing effect for large OD gas

Increasing theOD of atom cloud