skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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 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 aremore » 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.« less

Authors:
;  [1];  [2];  [2]
  1. Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7 (Canada)
  2. Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305 (Japan)
Publication Date:
OSTI Identifier:
20976540
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 74; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.74.063626; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Taylor, E, Griffin, A, Fukushima, N, Ohashi, Y, and Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama, 223. Pairing fluctuations and the superfluid density through the BCS-BEC crossover. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.74.063626.
Taylor, E, Griffin, A, Fukushima, N, Ohashi, Y, & Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama, 223. Pairing fluctuations and the superfluid density through the BCS-BEC crossover. United States. https://doi.org/10.1103/PHYSREVA.74.063626
Taylor, E, Griffin, A, Fukushima, N, Ohashi, Y, and Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama, 223. Fri . "Pairing fluctuations and the superfluid density through the BCS-BEC crossover". United States. https://doi.org/10.1103/PHYSREVA.74.063626.
@article{osti_20976540,
title = {Pairing fluctuations and the superfluid density through the BCS-BEC crossover},
author = {Taylor, E and Griffin, A and Fukushima, N and Ohashi, Y and Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama, 223},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.74.063626},
url = {https://www.osti.gov/biblio/20976540}, journal = {Physical Review. A},
issn = {1050-2947},
number = 6,
volume = 74,
place = {United States},
year = {2006},
month = {12}
}