Frequency shift and mode coupling of the collective modes of superfluid Fermi gases in the BCS-BEC crossover

Abstract

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.