Harmonically trapped quasi-two-dimensional Fermi gases with synthetic spin-orbit coupling

We study the properties of spin-orbit coupled and harmonically trapped quasi-two-dimensional Fermi gas with tunable s-wave interaction between the two spin species. We adapt an effective two-channel model which takes the excited states occupation in the strongly confined axial direction into consideration by introducing dressed molecules in the closed channel, and use a Bogoliubov- de Gennes （BdG） formalism to go beyond local density approximation. We find that both the in-trap phase structure and density distribution can be significantly modified near a wide Feshbach resonance compared with the single-channel model without the dressed molecules. Our findings will be helpful for the experimental search for the topological superfluid phase in ultracold Fermi gases.