The Efimov Effect in Ultracold Gases

Weakly Bounds Systems in Atomic and Nuclear PhysicsMarch 8 - 12, 2010

Institut für Experimentalphysik, Universität Innsbruck

Martin Berninger, Francesca Ferlaino, Alessandro Zenesini, Walter Harm, Hanns-Christoph Nägerl, Rudi Grimm

The Efimov Puzzle (an experimentalists view...)

TheoryExperimentEfimov States in the molecules and nuclei, Rome 2009Weakly-Bound Systems in Atomic and Nuclear Physics, Seattle 2010

Outline

• Introduction atomic few-body physics• The Efimov scenario• Experimental Efimov physics with Cs• Overview experimental Efimov physics• New results in caesium samples

(preliminary)

• Collisions in Dimer-Dimer samples• Ultracold exchange reactions

last bound level

y(r) halo dimer

kHz

2

2

maEb

2-body

CsCs

4-body

Cs2 Cs2

Cs2

CsCs

Cs3 Cs

Cs CsCsCs

Few-body physics

3-bodyCs2

CsCsCsCs

In general complex problem:• strong dependence on potential

kka

k

)(tanlim 0

0

manyvib.

levels

non-universal dimer

U(r)~1/r6

r

U(r)

schematic drawingTHz

Universal regimescattering length a>>r0

r0: range of the potentialr0 ~ lvdW ~ 100a0 for Cs

s wave scattering length:

dimers trimers tetramers

Universal connection:

?Halodimers

Efimovtrimers

Universaltetramers

Ultracold atomic gases as a model system

nT3 1

1

T 2h2

mkBT

Quantum gas

Classical gasT ~ 1µK – 20nK

Temperature

Control knobs

Interactions

Interaction strength a

crossed-beam trap

wy ≈ wz ≈ wx

3D 2D 1D

Geometry optical lattice

„pancake“ trap

Mixtures

• different interactions• different mass ratios• Bosonic / Fermionic systems

State

mF=3

F=3

mF=4F=4

32

MW transfer

caesium

magnetic moment of bound statediffers from the magnetic moment of the incident channel

B

a

abg

B0

F=3+F=3

F=3+F=4

F=4+F=4

(example Cs)

r

U(r)

incident channel

bound state

2

2

bgb ma

E

Tunable interaction:

Feshbach resonance

Magnetic tunability of the scattering length

energya < 0 a > 0

a/1

Two-particle picture

attractive repulsive

halodimer

s-wave resonances for Cs in F1=3 F2=3 channel

50 G 100 G

-1000

1000

2000

-2000

3000

0

magnetic field (G)

scat

terin

g le

ngth

(a 0

)

0 150 G

s-wave + d-wave resonances in Cs

bound state in open channel: EB~10kHzbackground scattering length abg~2000a0

EbB

44(6) 34(7) 34(6)F1 F2 (F1+F2)E. Tiesinga et al.

energya < 0 a > 0

The Efimov scenario

„Efimov – states“

halodimer

×22.7

×(22.7)2

...there exists an infinite series of weakly bound trimer states for resonant

two-body interaction...V. Efimov, Phys. Lett. B 33, 563-664 (1970)

weakly bound trimer

even more weaklybound trimer

a/1

a < 0

deeply bound dimer

Trap loss

energy3

3 AA nLn

3-atomic Efimov resonance

OFF resonance

ON resonancenew decay channel Enhancement of losses

10nK

200nK

3-Atomic Efimov resonance

Kraemer et al., Nature 440, 315 (2006)

three-body recombination rate

33 AA nLn

aLm

4

1

33 32

a4

recombination length:

energy

Ultracold sample of 133Cs atomsin atomic ground state: F=3, mF=3N ~ 105 atomsT = 10/200nK

3-atomic Efimov resonance

10nK

200nK

3-Atomic Efimov resonance

Kraemer et al., Nature 440, 315 (2006)

three-body recombination rate

33 AA nLn

aLm

4

1

33 32

a4

recombination length:

energy

20

2 sinh)]/ln([sin)2sinh(4590)(

aasaC

43 )(3 a

maCL

• for a<0, a :

C(a)=C(22.7a)

Braaten & Hammer

am

aCAD)(

*2

*02

*

sinh)]/ln([sin)2sinh(2.10)(

aas

aCAD

• for a>0, a :

)]/ln([(cos1.67)( 0

22 aaseaC

)1(8.16))2sinh( 4 e

Atom-Dimer relaxation rate :s0=1.00624

Braaten-Hammer theory

aAAA=-850 a0 amin=210 a0

L3max=5.7*10-22 cm6/s

L3min=1.33*10-28 cm6/s

3-atomic Efimov resonance

energyE

20

2 sinh)]/ln([sin)2sinh(4590)(

aasaC

43 )(3 a

maCL

• for a<0, a :

C(a)=C(22.7a)

Braaten & Hammer

am

aCAD)(

*2

*02

*

sinh)]/ln([sin)2sinh(2.10)(

aas

aCAD

• for a>0, a :

)]/ln([(cos1.67)( 0

22 aaseaC

)1(8.16))2sinh( 4 e

Atom-Dimer relaxation rate :s0=1.00624

a > 0

halodimer

a/1

s-wave state

d-wavestate

# dimer: ~ 4000# atoms: (3-6)x104

T = 30-300 nK

Separate atoms and dimers by magnetic gradient field before imaging

Measure the time-evolution & extract atom-dimer relaxation rate coefficient

Production of 6s-molecules viaFeshbach association

Atom-dimer Efimov resonance

Atom-dimer resonance at B=25 G aAD=+400 a0

• universality a>0 and a<0 via a=0 ?• transition universal to non-universal ? (r0~100a0)• any relation to Efimov physics at different

Feshbach resonances (@800G)?

Universal relation via pole:)1'()'()( 7.2206.1/ nnn

AAAn

AD aa

for n=0, n‘=1 aAD/aAAA= 0.47

Knoop et. al., Nature Physics 5, 227 (2009)

1/a

a < 0 a > 0

Atom-dimer Efimov resonance

energya < 0 a > 0

Tetra1

Tetra2

The extended Efimov scenario

Prediction of twouniversal 4-body statestied to each Efimov trimer!

H. Hammer and L. Platter, Eur. Phys. J. A 32, 113 (2007)J. von Stecher, J. P. D’Incao, and C. H. Greene, Nature Physics 5, 417 - 421 (2009)

F. Ferlaino et. al., PRL 102, 140401 (2009)

Tetra1 Tetra2

thold=250ms thold=8ms

Four-body states - experimental results

Experiment ~ 0.47 a*T

~ 0.84 a*T

Position of theuniversal 4-body states

Theorya*Tetra1 ~ 0.43 a*T

a*Tetra2 ~ 0.9 a*T

4-bodymixed3-body

Fitting functionsimple 3 body

simple 4 body

3 + 4 body

44

33 AAA nLnLn

F. Ferlaino et. al., PRL 102, 140401 (2009)

Tetra1 Tetra2

thold=250ms thold=8ms

Four-body states - experimental results

44

33 AAA nLnLn

Experiment ~ 0.47 a*T

~ 0.84 a*T

Position of theuniversal 4-body states

Theorya*Tetra1 ~ 0.43 a*T

a*Tetra2 ~ 0.9 a*T

Overview experimental Efimov physics

Barontini et al., Phys. Rev. Lett. 103, 043201 (2009)

Ottenstein et al., Phys. Rev. Lett. 101, 203202 (2008)Huckans et al., Phys. Rev. Lett. 102, 165302 (2009)Williams et al., Phys. Rev. Lett. 103, 130404 (2009)Wenz et al., Phys. Rev. A 80, 040702(R) (2009)

41K + 87Rb

6Li

Fermionic systems

Bosonic mixtures

Bosonic systems

Zaccanti et al., Nature Physics 5, (2009)

Pollack et al., Science 326 (2009)Gross et al., Phys. Rev. Lett 103, 163202 (2009)

Kraemer et al., Nature 440, 315 (2006)Knoop et. al., Nature Physics 5, 227 (2009)F. Ferlaino et. al., Phys. Rev. Lett. 102, 140401 (2009)

133Cs

39K7Li F=1, mF=1

F=1, mF=0

Successive Efimov Features – bosonic system (39K)

Zaccanti et al., Nature Physics, Vol. 5 (2009)

Florence-Group

Comparison with universal theory:Valid only for |a|>>r0

Model for finite-range interactions?

Res:

second order process: A+A+A D*+AaAD* losses in an atom sampledue to elastic scattering

Loss a (a0)

a<03B Max a1

- -1500

4B Max aT* -650

a>03B Min

a1+ 224

a2+ 5650

AD Maxa1* 30

a2* 930

Experiment with 39K atomic sampleacross Feshbach resonance, r0=64a0

atomic threshold

Usually, in the three-body process 3 particles are lost

Efimov physics in 39K: AD resonances

Thanks to M. Zaccanti & Co-Workers for the slides!

…but if AD cross section is large particle losses can be >>3!!!

Efimov physics in 39K: AD resonances

Thanks to M. Zaccanti & Co-Workers for the slides!

Successive Efimov Features – bosonic system (7Li – F=1,mF=1)Rice-Groupatomic sample 7Li (F=1,mF=1) across Feshbach resonance, r0=33a0

Pollack et al., Science 326 (2009)

Comparison universal theoryValid only for each side, systematic discrepancy (factor 2) Variation in the short range

phase acrossthe Feshbach resonance?

Loss a (a0) a (a0)

a<0

3B Max a1- -298 a2

- -6301

4B MaxaT

1,1 -120 aT1,2 -295

aT2,1 -2950 aT

2,2 -6150

a>0

3B Mina1

+ 224

a2+ 5650

AD Maxindirect a2* 608

DD Maxdebate

a*2,1 1470

a*2,2 3910

Res:a>0

a<0

a

Ottenstein et al., PRL 101, 203202 (2008)Huckans et al., PRL 102, 165302 (2009)Williams et al., PRL 103, 130404 (2009)Wenz et al., PRA 80, 040702(R) (2009)Braaten et al., PRL 103, 073202 (2009)Naidon et al., PRL 103, 073203 (2009)Floerchinger et al., PRA 79, 053633 (2009)Braaten et al., PRA 81, 013605 (2010)

Jochim & O‘Hara6Li 3 componentFermi-Spin-mixture:

|3> mF= -3/2|2> mF= -1/2|1> mF= 1/2

Comparison with universal theoryUsing fit results for high field resonance (895G)reproduces low field resonances accurately: 125(3)G & 499(2)GÞ No change in the three body parameter

for B ~ 750G? for aij ~ lvdw?

Efimov features in fermionic spin mixtures (6Li)

Loss state B(G)

a<0 3B Max

n=0 127

n=0 500

n‘=1 895

Res:

Gross et al., PRL 103, 163202 (2009)

Khaykovich-Groupatomic sample 7Li (F=1,mF=0)across Feshbach resonance

Comparison with universal theory:a+/|a-| = 0.92(14) (Theory=0.96(3))

Why does 7Li agree so nicely in (F=1,mF=0) and not in (F=1,mF=1)?

Bosonic system showing universality (7Li – F=1,mF=0)

Loss a (a0)

a<0 3B Max a- -264

a>0 3B Min a+ 1160

Results:

Barontini et al., Phys. Rev. Lett. 103, 043201 (2009)

Efimov Resonances – Heteronuclear systems (41K + 87Rb)

Florence-GroupSystem composed of distinguishable particles with different masses

Experiment with bosonic mixture of 41K and 87Rbat a interspecies Feshbach resonance Two resonantly interacting pairs are

sufficient for Efimov physics Existence of two Efimov series:

KRbRb: exp(/s0) = 131KKRb: exp(/s0) = 3.51105

Results:

KKRb-resonance

Loss a (a0)

a<03B Max KRbRb -246

3B Max KKRb -22000

a>0AD Maxindirect

a* 667

No oscillations for a>0 observed

K3

scattering length

900

K3

B(G)800

6d6

B (Gauss)

preliminary

K3

preliminaryLifetime measurements @ high magnetic fields

Recombination rate @ 6s6 resonance ~ 800G, width ~ 90GT~200nK

Resonance!

23

5max3 )(

844Tkm

LB

Unitarity limit:

Another piece to the puzzle!

L 3L 3

f l mf

nD= -L2 nD 2Measuring relaxation rate L2:

Ferlaino et al., PRL 101, 023201 (2008)

Experimental results: dimer-dimer collisions

s-wave state

d-wavestate

2 atoms in F=3, mF=3 microwaveSample of universal dimers in 6s-state: crossed dipole trap (1060nm) ND ~ 4000 T ~ 40 – 350 nK kBT << EB ~ h50kHz << EvdW ~ h2.7MHz

105 ultracold 133Cs atoms (40nK) Feshbach associationÞ Removal of atoms with microwaveÞ Sample of ultracold dimers

0 200 400 600 800 1000

0,1

1

120 nK

re

laxa

tion

rate

(10-1

0 cm

3 /s)

scattering lenght (a0)0 200 400 600 800 1000

0,1

1

80 nk

re

laxa

tion

rate

(10-1

0 cm

3 /s)

scattering lenght (a0)0 200 400 600 800 1000

0,1

1

40 nK

re

laxa

tion

rate

(10-1

0 cm

3 /s)

scattering lenght (a0)scattering length (a0)

.~L,1~1~ 22/1 constvTv inin

2-body reaction cross section (Wigner 1948)

energya < 0 a > 0

Tetra1Tetra2 ?

Exchange reactions with distinguishable particles

B + A2

F=4, mF=2, 3 or 4 Feshbach molecule / halo dimer2x (F=3, mF=3)

mF=3

F=3

F=4 2

mF=43

MW transfer

A + A2

F=3, mF=3

?

total lossexchange

T=50 nK

: atom-dimer loss rate coefficient

Exchange reactions loss rates

Knoop et al., Phys. Rev. Lett. 104, 053201 (2010) Theory: Jose D’Incao & Brett Esry

B

E

A+A+B

A2+B

A+ABE

new decay channel

mF=4

mF=3mF=2

resonance @ 35 G:opening exchange channel

B

EA+B

A+A

AB

A2

A2(v=-1)+B → A+AB(v=-1)

Closer look around 35 G

appearance of trapped atoms in state A!

Ultracold exchange reactioncontrolled by magnetic fieldT=100 nK, thold=22ms

mF=4

mF=3mF=2

Role of the large scattering length

A2(v=-1)+B

A+AB(v’<v)

A+AB(v=-1)

A2(v’<v)+B

A+A

A+B(mF=2)

A+B(mF=3)A+B(mF=4)

y(r)

2

2

maEb

2/ar

TheoryExperiment

Experimentalists wish list for Theory

Is there any relation for Efimov physics at different Feshbach resonances (133Cs low fields and Feshbach resonance @ 800G)?

Model for finite-range interactions, transition universal to non-universal (39K & 133Cs)?

Variation in the short range phase across the Feshbach resonance (7Li) – Factor 2?

Why does 7Li agree so nicely in (F=1,mF=0) and not in (F=1,mF=1)?

Why there is no change in the three body parameter in 6Li spin mixture for B ~ 750G and/or for aij ~ lvdw?

Coming soon:

Cs data for 800G resonance

Any connection of Efimov physics from a>0 to a<0 via a=0 (133Cs)? – Factor 1/2?

Temperature dependence in 133Cs halo molecules?

a << a

The Caesium-Efimov-Team

M.B.

Rudi Grimm

FrancescaFerlaino

AlessandroZenessini

Hanns-Christoph

Nägerl WalterHarm