Zeng-Qiang Yu

Institute for Advanced Study, Tsinghua University, Beijing, China

Collaborators: Hui Zhai, Shizhong Zhang

Reference: PRA 83, 041603(R) (2011); arXiv: 1105.2250v3

Lanzhou, Aug. 2011

Stability Conditions of a Strongly Interacting Boson-Fermion

Mixture across an inter-species Feshbach Resonance

23Na

stable conditions for a resonant many-body system:

(i) positive compressibility (ii) small atom loss

rate resonant Fermi gas: (yes )

BEC-BCS crossover

Stenger, et al., Phys. Rev. Lett. 82, 2422

resonant Bose gas: (no )

rapid atom loss (and collapse)

inter-species Feshbach resonance:

6Li-23Na, 6Li-85/87Rb, 40K-87Rb, 40K-41K …

BF

F

BF

B

Viverit, Pethick, and Smith, Phys. Rev. A 61, 053605

What if aBF

=∞ ?

three-body process

mechanical stability

mean-field theory:

Modugno, et al., Science 297, 2240; Stan, et al., PRL 93, 143001;

Inouye, et al., PRL. 93, 183201; Ospelkaus, et al., PRL 97, 120403;

F. Ferlaino, et al., PRA 73, 040702(R); Zaccanti, et al., PRA 77, 041605(R)

single-channel model

Pandharipande, Nucl. Phys. A 174, 641; Phys. Rev. C 7, 1312Cowell, et.al., Phys. Rev. Lett. 88, 210403

(non-perturbative )

(perturbative )

Jastrow-Slater wave-function

f(r): describe two-body correlation between a boson and a

fermion

LOCV (loweset order constraint variational)

approximation

A(η): dimensionless chemical potential of bosons, A(0) = -0.64

D(η): fraction of condensate depletion due to B-F interaction,

D(0) = 0.13

Condensation of Fermi polaron

stability conditions:

-5 -4 -3 -2 -1 0 1 20

0.2

0.4

0.6

k F a

BB

collapse

stable

mB = m

F

Mean-field collapse boundary

weakly-dependent on nB/nFcritical

crit

ical k F

aB

BnB / nF1 / (kFaBF)

Spin-Orbit Coupled Fermi Gases across a Feshbach Resonance

single-particle Hamiltonian

density of state (DoS)

H0 =X

p

³cyp" cy

p#

´ µ²p

¸m(px ¡ ipy)

¸m(px +ipy) ²p

¶ µcp"

cp#

¶

=X

p

h»p;+hy

p;+hp;+ +»p;¡ hyp;¡ hp;¡

i

µhp;+

hp;¡

¶=

1p

2

µ1 e¡ i' p

ei ' p ¡ 1

¶ µcp;"

cp;#

¶; »p;§ = ²p §

¸m

p?

2 1 0 1 2px

1

2

3

4Ep

N(E

)

E

free Fermi gas

bound state for any arbitrary weak attractive

interaction

PRB, 83, 094515

(2010)

finite center-of-mass momentum q

for small q

In-plane effective mass

Mean-feild transition temperature TBCS enhanced by DoS

effect

Molecular BEC temperature

Related works: arXiv:1104.5633; arXiv: 1105.1796 ; arXiv:

1105.2488; arXiv: 1106.0473; arXiv: 1106.0453; arXiv: 1106.3613;

arXiv: 1106.5667

arXiv: 1105.2250v3

Thanks for your attention.Thanks for your attention.

transition to mixture of atomic and molecular Fermi

liquid

similar to the polaron-molecule transition in imbalanced

Fermi gas

transition is estimated by

EM: mean-field energy of molecular state

further issue:

- details of the transition: condensate + 1 FS --> 2 FS

- phase diagram at finite temperature