Non-Hermitian topological superfluidity in a three-dimensional Fermi gas with spin-orbit coupling.

The experimental realizations of artificial spin-orbit coupling (SOC) and non-Hermitian potentials in ultracold atoms provide a versatile platform for exploring their interplay in quantum many-body systems. Here, we investigate a two-component Fermi gas in a three-dimensional cubic lattice with Rashba SOC and a complex-valued interaction arising from two-body loss. Based on a non-Hermitian mean-field theory, this work elucidates the interplay of dissipation and SOC in the pairing behavior of Fermi gases. Dissipation not only drives a phase transition from a superfluid to a normal state and induces a reentrant superfluid but also, synergistically with SOC, significantly expands the stability regions of both the normal and metastable superfluid phases. Moreover, the introduction of a Zeeman field can drive the system into a topological superfluid phase characterized by a nontrivial topological invariant. These results thereby uncover a rich spectrum of pairing phenomena in this dissipative quantum system.