Collective modes of quasi-one- and quasi-two-dimensional superfluid Fermi gases in a BCS–BEC crossover

We investigate the collective excitations of low-dimensional ultracold Fermi gases in the crossover between Bardeen–Cooper–Schrieffer (BCS) superfluid and Bose–Einstein condensation (BEC). We solve exactly the reduced hydrodynamic equations describing the dynamics of collective modes in quasi-one and quasi-two dimensions and provide analytical expressions of all eigenfrequencies and eigenfunctions, which are valid for both BCS and BEC limits and also for the whole crossover regime. All analytic results cover the known ones reported in literature for the BEC limit.