  The superfluid density is a fundamental quantity describing the response to a
rotation as well as in two-fluid collisional hydrodynamics. We present
extensive calculations of the superfluid density \rho_s in the BCS-BEC
crossover regime of a uniform superfluid Fermi gas at finite temperatures. We
include strong-coupling or fluctuation effects on these quantities within a
Gaussian approximation. We also incorporate the same fluctuation effects into
the BCS single-particle excitations described by the superfluid order parameter
\Delta and Fermi chemical potential \mu, using the Nozi\`eres and Schmitt-Rink
(NSR) approximation. This treatment is shown to be necessary for consistent
treatment of \rho_s over the entire BCS-BEC crossover. We also calculate the
condensate fraction N_c as a function of the temperature, a quantity which is
quite different from the superfluid density \rho_s. We show that the mean-field
expression for the condensate fraction N_c is a good approximation even in the
strong-coupling BEC regime. Our numerical results show how \rho_s and N_c
depend on temperature, from the weak-coupling BCS region to the BEC region of
tightly-bound Cooper pair molecules. In a companion paper by the authors
(cond-mat/0609187), we derive an equivalent expression for \rho_s from the
thermodynamic potential, which exhibits the role of the pairing fluctuations in
a more explicit manner.
