Dark lump excitations in superfluid Fermi gases

We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases.A Kadomtsev-Petviashvili I(KPI) solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen-Cooper-Schrieffer(BCS) regime,Bose-Einstein condensate(BEC) regime,and unitarity regime.Onelump solution as well as one-line soliton solutions for the KPI equation are obtained,and two-line soliton solutions with the same amplitude are also studied in the limited cases.The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.     

Ground-State Properties of Superfluid Fermi Gas in Fourier-Synthesized Optical Lattices

By employing the balance condition between the lattice potential and the interatomic interaction, we study the ground state solutions of superfluid Fermi gases in Fourier-synthesized （FS） optical lattices. The average energy of the ground state, the atoms number, and the atom density distribution of the Fermi system are analytically derived along the Bose–Einstein condensation （BEC） side to the Bardeen–Cooper–Schrieffer （BCS） side. We analyze the properties of ground state solutions at both the BEC limit and unitarity in FS optical lattices. It is found that the relative phase α between the two lattice harmonics impacts greatly on the properties of the ground state of the superfluid Fermi gas. Especially in the BCS limit, when α=π/2, the average energy presents an exponential form with the increase of the potential depth of the lattice harmonics v2. Meanwhile, there exits a minimal value. Moreover, due to the Fermi pressure, the atom density distribution at unitarity is more outstretched than that in the BEC limit. The average energy at unitarity is apparently larger than that in the BEC limit. The properties of the ground state solution exhibit very different behaviors when the system transits from the BEC side to the BCS side.     

Self-trapping and Macroscopic Tunnelling of Superfluid Fermi Gases in Multi-well Potentials

We study the tunnelling dynamics of superfluid Fermi gases trapped in multi-well system along the BEC-BCS crossover. Within the hydrodynamical model and by using the multi-mode approximation, the self-trapping dynamics of superfluid Fermi gases in multi-well system are obtained numerically. We find that the self-trapping to diffusion transition strongly depends on the well number. When the well number is less than three, the self-trapped state takes place easier on the BEC side than that on the BCS side. However, when the well number is larger than three, the self-trapped state takes place easier on the BCS side instead of the BEC side. Furthermore, by considering a superfluid of 40K atoms, we obtain the zero-mode and π-mode Josephson frequencies of coherent atomic oscillations in double-well system. It is noteworthy that the Josephson mode, especially, the existence of π-mode frequency strongly depends on the atoms number on the BCS side.     

Quantum Droplets in a Mixture of Bose–Fermi Superfluids

We study the formation of quantum droplets in the mixture of a single-component Bose–Einstein condensate(BEC),and a two-species Fermi superfluid across a wide Feshbach resonance.With repulsive boson-boson and attractive boson-fermion interactions,we show that quantum droplets can be stabilized by attractive fermionfermion interactions on the Bardeen–Cooper–Schrieffer(BCS) side of the resonance,and can also exist in the deep BEC regime under weak boson-fermion interactions.We map out the phase diagram for stable droplets with respect to the boson-boson and boson-fermion interactions,and discuss the role of different types of quantum fluctuations in the relevant regions of the BCS-BEC crossover.Our work reveals the impact of fermion pairing on the formation of quantum droplets in Bose–Fermi mixtures,and provides a useful guide for future experiments.     

Impurity-induced Shiba bound state in the BCS–BEC crossover regime of two-dimensional Fermi superfluid

For a two-dimensional ultra-cold Fermi superfluid with an effective static magnetic impurity, we theoretically investigated the variation of the Yu–Shiba–Rusinov(YSR) bound state in the Bardeen–Cooper–Schrieffer(BCS) to Bose–Einstein condensation(BEC) crossover regime.Within the framework of mean-field theory, analytical results of the YSR bound state energy were obtained as a function of the interaction parameters.First, when the background Fermi superfluid system stays in the weakly interacting BCS regime, we found that the YSR bound state energy is linearly dependent on the gap parameter with its coefficient slightly different from previous results.Second, we discovered re-entrance phenomena for the YSR state and an upper bound of the strength of the interaction between the paired atoms.By carefully analyzing the bound state energy as a function of the interaction parameters, we obtained a phase diagram showing the existence of the YSR state.Finally, we concluded that the re-entrance phenomena and the critical point can be easily experimentally detected through measurement of radio-frequency spectroscopy and density of states using current experimental techniques.     

Topological superfluid in a two-dimensional polarized Fermi gas with spin-orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional(2 D) polarized Fermi gas with spin–orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin–orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen–Cooper–Schrieffer(BCS) mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin–orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here,we focus on the region of BCS pairing and ignore the Fulde–Ferrell–Larkin–Ovchinnikov state.     

Entanglement dynamics in two-component Bose--Einstein condensates

Based on the exact solution of the time-dependent Schrodinger equation for two-species Bose-Einstein condensates （BECs） consisting of two hyperfine states of the atoms coupled by a tuned adiabatic and time-varying Raman coupling, we obtain analytically the entanglement dynamics of the system with various initial states, particularly the SU（2） coherent state, for both of cases with and without the nonlinear interactions. It is shown that the effect of nonlinear interaction on the entanglement appears only in a longer time period depending on the BEC parameters.     

Condensate fraction of asymmetric three-component Fermi gas

In this paper, we investigate the condensate fraction （CF） of fermionic pairs in the BCS-BEC crossover for three- component Fermi gas with both asymmetric interactions and unequal chemical potentials in two-dimensional free space. By using the functional-path-integral method, we have analytically derived the number densities and bound-state energy, from which the off-diagonal long-range order is analyzed in terms of the asymptotic behavior of the two-body density matrix. The explicit formula of CF is obtained as a function of the bound-state energy and population imbalance. It is demonstrated that the CF spectrum with respect to the bound-state energy can be used to characterize the quantum phase transition between the two kinds of Sarma phases as well as the transition from three-component to two-component superfluid. Moreover we obtain the same analytic formula of CF in the BCS superfluid phase as that of homogeneous Fermi gas with equal chemical potentials.     

Bright Soliton Solutions in Degenerate Femi Gas near Feshbach Resonance

For molecular and standard Bose-Einstein condensates and Fermi gases near Feshbach resonances, the general polytropic equation of states is P∝n γ＋1. According to the effective power γ≈0.5~1.3, we resolve the time-dependent nonlinear Schrodinger equation and find series bright solitons. The analysis could help in the search for matter-wave soliton trains in degenerate Femi gas.     

Collective Modes of a Quasi-Two-Dimensional Superfluid Fermi Gas in BCS-BEC Crossover

We investigate the collective modes of a quasi-two-dimensional （Q2D） superfluid Fermi gas in Bardeen-Cooper-Schrieffer Bose-Einstein condensation （BCS-BEC） crossover. For solving a generalized Gross-Pitaevskii equation by using a time-dependent variational method, we take a trial wavefunction with the form of hybrid Gaussianparabolic type, which not only reflects the Q2D character of the system and also allows an essentially analytical approach of the problem. We present a Q2D criterion that is valid for various superfluid regimes and displays clearly the relation between the maximum condensed particle number and the parameters of trapping potential as well as atom-atom interaction. We show that due to the small particle number in the Q2D condensate, the contribution to oscillating frequencies by the quantum pressure in the strong confinement direction is significant and hence a Thomas-Fermi approximation can not be used.