# Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction

## TL;DR

This paper develops a mean-field theory for non-Hermitian fermionic superfluids with complex interactions, revealing unique phase transitions and the effects of dissipation on superfluid properties.

## Contribution

It introduces a novel NH gap equation and uncovers unconventional phase transitions driven by non-Hermitian effects in fermionic superfluids.

## Key findings

- Superfluidity exhibits reentrant behavior with increasing dissipation.
- Superfluid gap is enhanced by dissipation in the strong interaction regime.
- Unique phase transitions are linked to exceptional points in the quasiparticle spectrum.

## Abstract

Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering between fermions. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are different from the standard BCS ones due to the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: superfluidity shows reentrant behavior with increasing dissipation, as a consequence of non-diagonalizable exceptional points, lines, and surfaces in the quasiparticle Hamiltonian for weak attractive interactions. For strong attractive interactions, the superfluid gap never collapses but is enhanced by dissipation due to an interplay between the BCS-BEC crossover and the quantum Zeno effect. Our results lay the groundwork for studies of fermionic superfluidity subject to inelastic collisions.