  We investigated effects of a Rashba-type spin-orbit coupling (SOC) on the
condensed density and superfluid density tensor of a two-component Fermi gas in
the BCS-BEC crossover at zero temperature. In anisotropic three dimensions
(3D), we found that SOC has an opposite effect on condensation (enhanced) and
superfluidity (suppressed in the SOC direction) and this effect becomes most
pronounced for very weak interactions and the SOC strength being larger than a
characteristic value. Furthermore, as functions of SOC strength, the condensed
density changes monotonously for all interaction parameters while the
superfluid density has a minimum when the interaction parameter is below a
critical value. We also discussed the isotropic two dimensional (2D) case where
analytical expressions for the gap and number equations were obtained and the
same phenomena was found as that of the 3D case.
