Population imbalanced Fermi gases in quasi two dimensions

We study s-wave pairing of population imbalanced Fermi atoms in quasi two dimensions using a mean-field theory. At zero temperature, we map out the phase diagram in the entire Bardeen, Cooper and Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover region by investigating the effect of weak atom tunnelling between layers. We find that the superfluid phase stabilizes as one decreases the atom tunnelling between layers. This allows one to control the superfluid-normal first-order phase transition by tuning a single experimental parameter. Further, we find that a tunnelling induced polarized superfluid phase appears in a narrow parameter region in the BEC regime. At finite temperatures, we use a Landau-Ginzberg functional approach to investigate the possibility of a spatially inhomogeneous Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in the weakly interacting BCS limit near the tricritical point of spatially homogenous superfluid, FFLO and normal phases. We find that the normal-FFLO phase transition is the first-order transition as opposed to the continuous transition predicted in zero-temperature theories.