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Title: Collective modes of low-dimensional superfluid Fermi gases in the BCS-BEC crossover: Time-dependent variational analysis

Abstract

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.

Authors:
;  [1]
  1. Department of Physics and Institute of Theoretical Physics, East China Normal University, Shanghai 200062 (China)
Publication Date:
OSTI Identifier:
20982162
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.023611; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; ATOMS; BCS THEORY; BOSE-EINSTEIN CONDENSATION; CONDENSATES; CONFINEMENT; EXPANSION; FERMI GAS; FERMIONS; PARTICLES; POTENTIALS; SUPERFLUIDITY; TEMPERATURE RANGE 0000-0013 K; THOMAS-FERMI MODEL; TIME DEPENDENCE; TRAPPING; TWO-DIMENSIONAL CALCULATIONS; VARIATIONAL METHODS; WAVE FUNCTIONS

Citation Formats

Zhou, Yu, and Huang, Guoxiang. Collective modes of low-dimensional superfluid Fermi gases in the BCS-BEC crossover: Time-dependent variational analysis. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.023611.
Zhou, Yu, & Huang, Guoxiang. Collective modes of low-dimensional superfluid Fermi gases in the BCS-BEC crossover: Time-dependent variational analysis. United States. doi:10.1103/PHYSREVA.75.023611.
Zhou, Yu, and Huang, Guoxiang. Thu . "Collective modes of low-dimensional superfluid Fermi gases in the BCS-BEC crossover: Time-dependent variational analysis". United States. doi:10.1103/PHYSREVA.75.023611.
@article{osti_20982162,
title = {Collective modes of low-dimensional superfluid Fermi gases in the BCS-BEC crossover: Time-dependent variational analysis},
author = {Zhou, Yu and Huang, Guoxiang},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.75.023611},
journal = {Physical Review. A},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • 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-Poincare 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 bymore » choosing appropriate parameters of the system. The analytical results obtained are checked by numerical simulations and good agreement is found.« less
  • Using the coarse-grain averaged hydrodynamic approach, we calculate all low energy transverse excitation spectrum of a rotating Fermi superfluid containing vortex lattices for all regimes along the Bose-Einstein condensate-Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. In the fast rotating regime, the molecular BEC enters into the lowest Landau level, but the superfluid in the unitarity and the BCS regimes occupies many low-lying Landau levels. The difference between the breathing mode frequencies at the BEC and unitarity limit shrinks to zero as the rotation speed approaches the radial trap frequency, in contrast to the finite difference in the nonrotating systems.
  • We investigate the collective excitations of a harmonically trapped superfluid Fermi gas at varying coupling strengths across a BCS-BEC crossover. Using a hydrodynamic approach, we solve analytically the eigenvalue problem of collective modes and provide explicit expressions for all eigenvalues and eigenfunctions, which are valid for both BCS and BEC limits and also for the whole crossover regime. Both spherical- and axial-symmetric traps are taken into account, and the features of these collective modes in the BCS-BEC crossover are discussed and compared with available experimental and numerical data.
  • We perform a detailed study of the collective mode across the whole crossover from the Bose-Einstein condensate (BEC)-to the BCS regime in fermionic gases at zero temperature, covering the whole range of energy beyond the linear regime. This is done on the basis of the dynamical BCS model. We recover first the results of the linear regime in a simple form. Then specific attention is paid to the nonlinear part of the dispersion relation and its interplay with the continuum of single-fermionic excitations. In particular we consider in detail the merging of the collective mode into the continuum of single-fermionicmore » excitations. This occurs not only on the BCS side of the crossover, but also slightly beyond unitarity on the BEC side. Another remarkable feature is the very linear behavior of the dispersion relation in the vicinity of unitarity almost up to merging with the continuum. Finally, while on the BEC side the mode is quite analogous to the Bogoliubov mode, a difference appears at high wave vectors. On the basis of our results we determine the Landau critical velocity in the BEC-BCS crossover which is found to be largest close to unitarity. Our investigation has revealed interesting qualitative features which deserve experimental exploration as well as further theoretical studies by more sophisticated means.« less
  • We construct a time-dependent Ginzburg-Landau (TDGL) theory for the superfluid atomic Fermi-gases near the Feshbach resonance from the fermion-boson model on the basis of the functional integral formalism. We show that the GL coefficients in the TDGL equation are complex numbers except in the BEC limit. The complex TDGL equation describes both damping and propagating dynamics, which leads to very rich superfluid dynamics near the Feshbach resonance. We predict multiple plane-wave modes corresponding to the in-phase and out-of-phase like oscillations between fermionic and bosonic superfluids and a galaxylike spiral pattern for a vortex.