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 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.
| Original language | English |
|---|---|
| Article number | 063626 |
| Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
| Volume | 74 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2006 |
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ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)
Cite this
Pairing fluctuations and the superfluid density through the BCS-BEC crossover. / Taylor, E.; Griffin, A.; Fukushima, N.; Ohashi, Yoji.
In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 74, No. 6, 063626, 2006.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Pairing fluctuations and the superfluid density through the BCS-BEC crossover
AU - Taylor, E.
AU - Griffin, A.
AU - Fukushima, N.
AU - Ohashi, Yoji
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevA.74.063626
DO - 10.1103/PhysRevA.74.063626
M3 - Article
AN - SCOPUS:33846384237
VL - 74
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 6
M1 - 063626
ER -