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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