Non-Hermitian (NH) quantum systems host exceptional points (EPs), where eigenstates and eigenvalues coalesce, leading to unconventional many-body phenomena absent in Hermitian systems. While NH fermionic systems with complex interactions exhibit superfluid (SF) breakdown with EPs, spin-dependent asymmetric hopping can stabilize a NH superfluid (NH-SF) that coexists with EPs. In this work, we investigate the quasi-one-dimensional NH attractive Fermi-Hubbard model by using NH-BCS theory. We demonstrate that, when the system is regarded as weakly-coupled chains, the exceptional SF phase becomes unstable and metastable (exceptional) SF state appears between the stable SF and normal states. In the one-dimensional limit, the exceptional SFs disappear entirely and EPs only appear on the phase boundary between the normal and SF states. These results reveal how dimensional crossover governs the stability of the exceptional SF, providing the insights into the interplay between dimensionality and dissipation, with potential relevance for experimental implications in ultracold atoms.
Takemori et al. (Sun,) studied this question.