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Zeng-Qiang Yu Institute for Advanced Study, Tsinghua University, Beijing, China

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.

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Zeng-Qiang Yu Institute for Advanced Study, Tsinghua University, Beijing, China

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  1. Stability Conditions of a Strongly Interacting Boson-Fermion Mixtureacross an inter-species Feshbach ResonanceSpin-Orbit Coupled Fermi Gases across a Feshbach Resonance 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

  2. Part I Stability Conditions of a Strongly Interacting Boson-Fermion Mixtureacross an inter-species Feshbach Resonance

  3. Resonant Many-Body System • stable conditions for a resonant many-body system: (i) positive compressibility (ii) small atom loss rate • resonant Bose gas: (no) • rapid atom loss (and collapse) • resonant Fermi gas: (yes) BEC-BCS crossover 23Na Stenger, et al., Phys. Rev. Lett. 82, 2422

  4. What about Boson-Fermion Mixture? • inter-species Feshbach resonance:6Li-23Na, 6Li-85/87Rb, 40K-87Rb, 40K-41K … 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) • three-body process B B F F B F • mechanical stabilitymean-field theory: What if aBF=∞ ? Viverit, Pethick, and Smith, Phys. Rev. A 61, 053605

  5. Theoretical Treatment • single-channel model (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 Pandharipande, Nucl. Phys. A 174, 641; Phys. Rev. C 7, 1312Cowell, et.al., Phys. Rev. Lett. 88, 210403

  6. Equation of State (EoS) 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

  7. Mechanical Stability Condition • stability conditions: critical weakly-dependent on nB/nF critical kFaBB nB / nF 1 / (kFaBF)

  8. Part II Spin-Orbit Coupled Fermi Gases across a Feshbach Resonance

  9. Spin-orbit coupling, single-particle level • single-particle Hamiltonian • density of state (DoS) free Fermi gas

  10. Two-body problem • 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

  11. BEC-BCS crossover, Universality (T=0)

  12. Crossover at finite temperature • 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

  13. Thanks for your attention. Thanks for your attention.

  14. Applicable Regime and Further Issue • 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

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