Fulde-Ferrell-Larkin-Ovchinnikov state to topological superfluidity transition in bilayer spin-orbit coupled degenerate Fermi gas

Recently a scheme has been proposed for generating the 2D Rashba-type spin-orbit coupling (SOC) for ultracold atomic bosons in a bilayer geometry [S.-W. Su et al, Phys. Rev. A textbf{93}, 053630 (2016)]. Here we investigate the superfluidity properties of a degenerate Fermi gas affected by the SOC in such a bilayer system. We demonstrate that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state appears in the regime of small to moderate atom-light coupling. In contrast to the ordinary SOC, the FFLO state emerges in the bilayer system without adding any external fields or spin polarization. As the atom-light coupling increases, the system can transit from the FFLO state to a topological superfluid state. These findings are also confirmed by the BdG simulations with a weak harmonic trap added.