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

## TL;DR

This paper explores how a bilayer spin-orbit coupled Fermi gas can transition from a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state to a topological superfluid state as atom-light coupling increases, revealing novel superfluid phases.

## Contribution

It demonstrates the emergence of FFLO and topological superfluid states in a bilayer SOC Fermi gas without external fields, expanding understanding of superfluid phase transitions.

## Key findings

- FFLO state appears at small to moderate atom-light coupling
- Transition from FFLO to topological superfluid with increasing coupling
- Confirmed results via BdG simulations with harmonic trap

## Abstract

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.