Quasi-two-dimensional Fermi gases at finite temperatures

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, radiofrequency 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) -> 0. Furthermore, our results suggest that T-c can be enhanced by relaxing the confinement and perturbing away from the 2D limit.