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Opposite effect of spin-orbit coupling on condensation and superfluidity

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.