Pairing fluctuations and the superfluid density through the BCS-BEC crossover

E. Taylor; A. Griffin; N. Fukushima; Y. Ohashi

doi:10.1103/PhysRevA.74.063626

paper

Pairing fluctuations and the superfluid density through the BCS-BEC crossover

arXiv:cond-mat/0609187 · doi:10.1103/PhysRevA.74.063626

Abstract

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 $ρ_{s}$ 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 $ρ_{s}$ all include the effect of fluctuations at the same level in a self-consistent manner. We show that the normal fluid density $ρ_{n} \equiv n - ρ_{s}$ naturally separates into a sum of contributions from Fermi BCS quasiparticles ( $ρ_{n}^{F}$ ) and Bose collective modes ( $ρ_{n}^{B}$ ). The expression for $ρ_{n}^{F}$ is just Landau's formula for a BCS Fermi superfluid but now calculated over the BCS-BEC crossover. The expression for the Bose contribution $ρ_{n}^{B}$ 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 $ρ_{s}$ using an expression equivalent to the one derived in this paper, over the BCS-BEC crossover, including unitarity, and at finite temperatures.

30 pages

Pairing fluctuations and the superfluid density through the BCS-BEC crossover

Abstract

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