  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 tunneling
between layers. We find that the superfluid phase stabilizes as one decreases
the atom tunneling 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 tunneling 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
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 first order transition as opposed to the continues transition
predicted in zero temperature theories.
