zeng-qiang yu institute for advanced study, tsinghua university, beijing, china
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Stability Conditions of a Strongly Interacting Boson-Fermion Mixture across an inter-species Feshbach Resonance Spin-Orbit Coupled Fermi Gases across a Feshbach Resonance. Zeng-Qiang Yu Institute for Advanced Study, Tsinghua University, Beijing, China. - PowerPoint PPT PresentationTRANSCRIPT
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