Superfluidity and collective modes in a uniform gas of Fermi atoms with a Feshbach resonance

We investigate strong-coupling superfluidity in a uniform two-component gas of ultra-cold Fermi atoms attractively interacting via quasi-molecular bosons associated with a Feshbach resonance. This interaction is tunable by the threshold energy 2ν of the Feshbach resonance, becoming large as 2ν is decreased (relative to 2εF, where εF is the Fermi energy of one component.). In recent work, we showed that the enhancement of this tunable pairing interaction naturally leads to the BCS-BEC crossover, where the character of the superfluid phase transition changes from the BCS-type to a BEC of composite bosons consisting of preformed Cooper-pairs and Feshbach-induced molecules. In this paper, we extend our previous work and study both single quasiparticles and the collective dynamics of the superfluid phase below the phase transition temperature Tc, limiting ourselves to a uniform gas. We show how the superfluid order parameter changes from the Cooper-pair amplitude ∆ to the square root of the number of condensed molecules (φm) associated with the Feshbach resonance, as the threshold energy 2ν is lowered. In the intermediate coupling regime, the superfluidity is shown to be characterized by an order parameter consisting of a superposition of ∆ and φm. We also discuss the Goldstone mode associated with superfluidity, and show how its character smoothly changes from the Anderson-Bogoliubov phonon in the BCS regime