bcs-bec crossover in cold atoms - university of …conferences.illinois.edu/bcs50/pdf/jin.pdf · d....
TRANSCRIPT
Investigate many-body quantum physics with a model system
Motivation: Why study atomic gases?
BEC
Mott insulator
Rapidly rotating BECs
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)
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