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

Abstract

We investigate the collective modes of a quasi-two-dimensional (Q2D)superfluid Fermi gas in Bardeen–Cooper–Schrieffer Bose–Einsteincondensation (BCS-BEC) crossover. For solving a generalizedGross–Pitaevskii equation by using a time-dependent variational method,we take a trial wavefunction with the form of hybrid Gaussian-parabolictype, which not only reflects the Q2D character of the system and alsoallows an essentially analytical approach of the problem. We present aQ2D criterion that is valid for various superfluid regimes and displaysclearly the relation between the maximum condensed particle number andthe parameters of trapping potential as well as atom–atom interaction.We show that due to the small particle number in the Q2D condensate, thecontribution to oscillating frequencies by the quantum pressure in thestrong confinement direction is significant and hence a Thomas–Fermiapproximation can not be used.