Quasi-two-dimensional Fermi gases at finite temperature

TL;DR

This paper investigates the properties of a quasi-two-dimensional Fermi gas with attractive interactions, calculating key thermodynamic quantities and superfluid transition temperature using a mean-field approach that includes all harmonic confinement levels.

Contribution

It extends mean-field theory to quasi-2D Fermi gases, providing a generalized critical temperature formula and insights into how confinement affects superfluidity.

Findings

The superfluid critical temperature $T_c$ is derived for quasi-2D gases.

Results show $T_c$ can be increased by relaxing confinement.

The theory reduces to known 3D results in the appropriate limit.

Abstract

We consider a Fermi gas with short-range attractive interactions that is confined along one direction by a tight harmonic potential. For this quasi-two-dimensional (quasi-2D) Fermi gas, we compute the pressure equation of state, radio frequency spectrum, and the superfluid critical temperature $T_c$ using a mean-field theory that accounts for all the energy levels of the harmonic confinement. Our calculation for $T_c$ provides a natural generalization of the Thouless criterion to the quasi-2D geometry, and it correctly reduces to the 3D expression derived from the local density approximation in the limit where the confinement frequency $\omega_z \to 0$. Furthermore, our results suggest that $T_c$ can be enhanced by relaxing the confinement and perturbing away from the 2D limit.