  We investigate strong-coupling superfluidity in a uniform gas of Fermi atoms
attractively interacting via quasi-molecular bosons associated with a Feshbach
resonance. This interaction is tunable by the threshold energy $2\nu$ of the
Feshbach resonance, becoming large as $2\nu$ is decreased. 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 quasi-particles and the collective
dynamics of the superfluid phase below Tc. We show how the superfluid order
parameter changes from the Cooper-pair amplitude to the square root of the
number of condensed molecules associated with the Feshbach resonance, as the
threshold energy $2\nu$ is lowered. 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 to the Bogoliubov phonon in
the BEC regime in the BCS-BEC crossover. This Goldstone mode is shown to appear
as a resonance in the spectrum of the density-density correlation function,
which is experimentally accessible.
