D. Jin

JILA, NIST and the University of Colorado

$ NSF, NASA, NIST

BCS-BEC Crossover in Cold Atoms

Investigate many-body quantum physics with a model system

Motivation: Why study atomic gases?

BEC

Mott insulator

Rapidly rotating BECs

Fermi superfluidity

Fermi condensate

Fermi gas in an optical lattice

Vortices

1. Create an ultracold Fermi gas

2. Realize and detect Cooper pairing

Challenges

1. True ground state is a solid.

2. Spin degree of freedom is frozen out.

3. Collisions/interactions are only s-wave.

Creating an ultracold Fermi gasUltracold (100 nK!) gas challenges:

spin ↑

spin ↓kT

Creating an ultracold Fermi gas

Collisions/interactions are only s-wave.

kT

non-s-wave

Spin-polarized fermions stop colliding.

R

s-wave

V(R)centrifugal

barrier

R

V(R)

Creating an ultracold Fermi gas

Use a stable mixture of two spin-states.

Fermions

T/TF=0.8

T/TF=0.3

T/TF=0.1

EF

40K

B. DeMarco and D. S. Jin, Science 285, 1703 (1999)

Apparatus

1. T/TF is not that low.

2. 40K atoms have weak, repulsive interactions.

3. Detecting the phase transition is not so easy.

Cooper pairing of atomsCooper pairing challenges:

BEC BCS?

Interactionss-wave scattering length, a

a > 0 repulsive, a < 0 attractiveLarge |a| → strong interactions

V(R)

R

a

Controlling interactions

0

scattering length, a

a > 0 repulsive, a < 0 attractiveLarge |a| → strong interactions

40K

A magnetic-field tunable atomic scattering resonance

Channels are coupled by the hyperfine interaction.

Magnetic-field Feshbach resonance

→ ←colliding atoms in channel 1

molecule state in channel 2

Ebinding

molecules

→ ←

attractive

repulsive

ΔB>

Magnetic-field Feshbach resonance

repulsive

free atoms

Magnetic-field Feshbach resonance

molecules

→ ←

attractive

repulsive

ΔB>

free atoms

s-wave scattering length, a

Ebinding

215 220 225 230-3000

-2000

-1000

0

1000

2000

3000

scat

terin

g le

ngth

(ao)

B (gauss)

Magnetic-field Feshbach resonance

C. A. Regal and D. S. Jin, PRL 90, 230404 (2003)

repulsive

attractive

spectroscopic measurement of the mean-field energy shift

Molecules!

220 221 222 223 224

-500

-400

-300

-200

-100

0

atoms molecules

Ene

rgy

(kH

z)

B (gauss)

Measured using rf photodissociation

C. Regal et al., Nature 424, 47 (2003)

Magnetic-field Feshbach resonance

molecules

→ ←

attractive

repulsive

ΔB>

free atoms

s-wave scattering length, a

Ebinding

Fermi Condensate2004

strongerattractive interactions

Imaging atom pairs

Bose-Einstein Condensate

C. A. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004)

BCS-BEC Crossover

1 0 -10

0.1

0.2

Interaction strength 1/kFa

Ent

ropy

T/T

F

-0.0200.0100.0250.0500.0750.1000.1250.1500.175

condensate fraction

00.01

0.05

0.1

0.15

C.A. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004)

1 0 -10

0.1

0.2

Interaction strength 1/kFa

Ent

ropy

T/T

F

-0.0200.0100.0250.0500.0750.1000.1250.1500.175

BCS-BEC Crossovercondensate

fraction0

a BCS-BEC crossover theory

Q. Chen, C.A. Regal, M. Greiner, D.S. Jin & K. Levin, PRA 73, 041601 (2006).

Initi

al

C.A. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004)

Probing the BCS-BEC crossover

Thermodynamic measurements

Vortices

Collective excitations

Probes ofpairing

Condensate fractionUnbalanced

spin population

1 0 -10

0.1

0.2

Interaction strength 1/kFa

Ent

ropy

T/T

F

Unitarity andUniversality

Correlations inatom shot noise

PeopleJ. Goldwin

M. Olsen

Brian DeMarco Cindy Regal Markus Greiner