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International Journal of Modern Physics B

Josephson dynamics of strongly interacting superfluid Fermi gases in double-well potentials

Ji Li, Wen Wen, Yuke Zhang, Xiaodong Ma

Published Dec 10, 2020• 2 citations
Publisher

Abstract

In this work, we study the nonlinear Josephson dynamics of Fermi superfluids in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a molecular Bose-Einstein condensate (BEC) in a double-well potential. Under a two-mode approximation, we derive a full two-mode (fTM) model including all interaction energy terms. By solving the fTM model numerically, we study the zero-phase and [Formula: see text]-phase modes of Josephson oscillations in the BCS–BEC crossover. We find that in the strongly interacting regime the cross interaction terms not appearing in the two-mode model cannot be easily ignored. The cross interactions can alter the behaviors of Josephson dynamics substantially, and interestingly the alterations for the zero-phase and [Formula: see text]-phase modes are just opposite.

DOI
10.1142/s0217979221500028

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In this work, we study the nonlinear Josephson dynamics of Fermi superfluids in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a molecular Bose-Einstein condensate (BEC) in a double-well potential. Under a two-mode approximation, we derive a full two-mode (fTM) model including all interaction energy terms. By solving the fTM model numerically, we study the zero-phase and [Formula: see text]-phase modes of Josephson oscillations in the BCS–BEC crossover. We find that in the strongly interacting regime the cross interaction terms not appearing in the two-mode model cannot be easily ignored. The cross interactions can alter the behaviors of Josephson dynamics substantially, and interestingly the alterations for the zero-phase and [Formula: see text]-phase modes are just opposite.
We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen—Cooper—Schrieffer (BCS) superfluid to Bose—Einstein condensates (BEC). Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the case of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.
By considering the contribution of the higher-order term representing the lowest approximation of beyond mean field corrections, we investigate a superfluid Fermi gas confined in a double-well potential in Bose–Einstein Condensation (BEC) side of the Bardeen–Cooper–Schrieffer (BCS) to BEC crossover. Two limited cases of deep BEC regime and BEC regime of BCS–BEC crossover, corresponding to the two-body scattering length a sc is small enough and large enough, respectively. We derive a simple two-mode model that could depict the dynamics effectively. With making thorough analysis on the two-mode model and its corresponding classical Hamiltonian, we find that the Josephson oscillation or self-trapping phenomenon could emerge at certain parameters. We find three kinds of the phase states: Josephson oscillation (JO), oscillating-phase-type self-trapping (OPTST) and running-phase-type self-trapping (RPTST). The dependence of these three phase states on the dimensionless interaction parameter y = 1/(kFa sc ) and the initial system energy are given in this paper.
Abstract In this work, we present a theoretical study for the collective oscillation modes, i.e. quadrupole, radial and axial mode, of a mixture of Bose and Fermi superfluids in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in harmonic trapping potentials with cylindrical symmetry of experimental interest. To this end, we start from the coupled superfluid hydrodynamic equations for the dynamics of Bose–Fermi superfluid mixtures and use the scaling theory that has been developed for a coupled system. The collective oscillation modes of Bose–Fermi superfluid mixtures are found to crucially depend on the overlap integrals of the spatial derivations of density profiles of the Bose and Fermi superfluids at equilibrium. We not only present the explicit expressions for the overlap density integrals, as well as the frequencies of the collective modes provided that the effective Bose–Fermi coupling is weak, but also test the valid regimes of the analytical approximations by numerical calculations in realistic experimental conditions. In the presence of a repulsive Bose–Fermi interaction, we find that the frequencies of the three collective modes of the Bose and Fermi superfluids are all upshifted, and the change speeds of the frequency shifts in the BCS–BEC crossover can characterize the different groundstate phases of the Bose–Fermi superfluid mixtures for different trap geometries.
We introduce a quasianalytic nonlinear Schr\"odinger equation with beyond mean-field corrections to describe the dynamics of a zero-temperature dilute superfluid Fermi gas in the crossover from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime, where kF∣a∣⪡1{k}_{F}|a|⪡1kF​∣a∣⪡1 with aaa the sss-wave scattering length and kF{k}_{F}kF​ the Fermi momentum, through the unitarity limit ${k}_{F}a\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$ to the Bose-Einstein condensation (BEC) regime where kFa>0{k}_{F}a>0kF​a>0. The energy of our model is parametrized using the known asymptotic behavior in the BCS, BEC, and the unitarity limits and is in excellent agreement with accurate Green's-function Monte Carlo calculations. The model generates good results for frequencies of collective breathing oscillations of a trapped Fermi superfluid.
We investigate collective modes and free expansions of quasi-one- and quasi-two-dimensional (Q1D and Q2D) ultracold Fermi gases in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). We solve a superfluid order parameter equation valid for the BCS-BEC crossover by employing a time-dependent variational method. We take a trial wave function of hybrid Gaussian-parabolic type, which not only reflects the low-dimensional character of the system but also allows an essentially analytical approach for the problem. We present Q1D and Q2D criteria that are valid in various superfluid regimes and show clearly the relation between the maximum condensed particle number and the parameters of the trapping potential as well as the atom-atom interaction. We demonstrate that, due to the small particle number in Q1D and Q2D condensates, the contribution to oscillating frequencies of collective modes by the quantum pressure in the strong-confinement direction is significant and hence the Thomas-Fermi approximation cannot be used. We also show that the free expansion of Q1D and Q2D superfluid Fermi gases in the strong-confinement direction is much faster than that in the weak-confinement direction.
We investigate the dynamical behavior of large-amplitude collective modes in a superfluid Fermi gas in the crossover from Bardeen--Cooper--Schrieffer (BCS) superfluid to Bose--Einstein condensate (BEC) based on a hydrodynamic approach. We first solve the superfluid hydrodynamic equations that describe the time evolution of fermionic condensates in the BCS-BEC crossover and calculate explicitly the frequency shifts of the collective modes induced by nonlinear effects using the Lindstedt--Poincar\'e method. The result shows that the frequency shifts display different features in different superfluid regimes. We then study the second-harmonic generation of the collective modes under a phase-matching condition, which can be fulfilled by choosing appropriate parameters of the system. The analytical results obtained are checked by numerical simulations and good agreement is found.