Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures

TL;DR

This paper presents comprehensive calculations of superfluid density and condensate fraction across the BCS-BEC crossover at finite temperatures, incorporating fluctuation effects for a consistent understanding of superfluid properties.

Contribution

The study introduces a unified approach including fluctuation effects via Gaussian and NSR approximations to accurately compute superfluid density and condensate fraction across the crossover.

Findings

Superfluid density  ho_s varies with temperature across the crossover.

Condensate fraction N_c remains well-approximated by mean-field even in strong coupling.

Results highlight the distinct behaviors of  ho_s and N_c with temperature.

Abstract

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.