  We investigate the properties of a spin-orbit coupled quasi-two-dimensional
Fermi gas with tunable s-wave interaction between the two spin species. By
analyzing the two-body bound state, we find that the population of the excited
states in the tightly-confined axial direction can be significant when the
two-body binding energy becomes comparable or exceeds the axial confinement.
Since the Rashba spin-orbit coupling that we study here tends to enhance the
two-body binding energy, this effect can become prominent at unitarity or even
on the BCS side of the Feshbach resonance. To study the impact of these excited
modes along the third dimension, we adopt an effective two-dimensional
Hamiltonian in the form of a two-channel model, where the dressed molecules in
the closed channel consist of the conventional Feshbach molecules as well as
the excited states occupation in the axial direction. With properly
renormalized interactions between atoms and dressed molecules, we find that
both the density distribution and the phase structure in the trap can be
significantly modified near a wide Feshbach resonance. In particular, the
stability region of the topological superfluid phase is increased. Our findings
are helpful for the experimental search for the topological superfluid phase in
ultra-cold Fermi gases, and have interesting implications for
quasi-low-dimensional polarized Fermi gases in general.
