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

Journal Article · Fri Dec 15 04:00:00 EST 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.74.063626· OSTI ID:20976540

Taylor, E; Griffin, A ^[1]; Fukushima, N ^[2]; Ohashi, Y ^[2]

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1. Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7 (Canada)
2. Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305 (Japan)

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 Nozieres and Schmitt-Rink, we use this definition of {rho}{sub 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}{sub s} all include the effect of fluctuations at the same level in a self-consistent manner. We show that the normal fluid density {rho}{sub n}{identical_to}n-{rho}{sub s} naturally separates into a sum of contributions from Fermi BCS quasiparticles ({rho}{sub n}{sup F}) and Bose collective modes ({rho}{sub n}{sup B}). The expression for {rho}{sub n}{sup 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}{sub n}{sup 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}{sub s} using an expression equivalent to the one derived in this paper, over the BCS-BEC crossover, including unitarity, and at finite temperatures.

• OSTI ID: 20976540
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 74; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
APPROXIMATIONS
BCS THEORY
BOGOLYUBOV METHOD
BOSE-EINSTEIN CONDENSATION
DENSITY
EXCITATION
FERMI GAS
FERMIONS
FLUCTUATIONS
GAUSSIAN PROCESSES
POTENTIALS
QUASI PARTICLES
SUPERFLUIDITY