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

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

30 pages

References in corpus (5)

• Weakly bound dimers of fermionic atoms
• Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
• BCS-BEC crossover in a system of microcavity polaritons
• Temperature of a trapped unitary Fermi gas at finite entropy
• Comparison between a diagrammatic theory for the BCS-BEC crossover and Quantum Monte Carlo results

Cited by in corpus (8)

• Theory of ultracold Fermi gases
• The effect of population imbalance on the Berezinskii-Kosterlitz-Thouless phase transition in a superfluid Fermi gas
• BCS-BEC crossover in a random external potential
• Variational theory of two-fluid hydrodynamic modes at unitarity
• Phase separation in imbalanced fermion superfluids beyond mean-field
• Imbalanced d-wave superfluids in the BCS-BEC crossover regime at finite temperatures
• Spin-polarized Fermi superfluids as Bose-Fermi mixtures
• The Josephson relation for the superfluid density in the BCS-BEC crossover