We derive an expression for the superfluid density of a uniform two-component Fermi gas through the BCS-BEC crossover in terms of the thermodynamic potential in the presence of an imposed superfluid flow. Treating the pairing fluctuations in a Gaussian approximation following the approach of Nozières and Schmitt-Rink, we use this definition of ρs to obtain an explicit result which is valid at finite temperatures and over the full BCS-BEC crossover. It is crucial that the BCS gap Δ, the chemical potential μ, and ρs all include the effect of fluctuations at the same level in a self-consistent manner. We show that the normal fluid density ρn n- ρs naturally separates into a sum of contributions from Fermi BCS quasiparticles (ρnF) and Bose collective modes (ρnB). The expression for ρnF is just Landau's formula for a BCS Fermi superfluid but now calculated over the BCS-BEC crossover. The expression for the Bose contribution ρnB is more complicated and only reduces to Landau's formula for a Bose superfluid in the extreme BEC limit, where all the fermions have formed stable Bose pairs and the Bogoliubov excitations of the associated molecular Bose condensate are undamped. In a companion paper, we present numerical calculations of ρs using an expression equivalent to the one derived in this paper, over the BCS-BEC crossover, including unitarity, and at finite temperatures.
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|Publication status||Published - 2006 Dec 1|
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics