Theory of non-Hermitian fermionic superfluidity subject to inelastic collisions in ultracold atoms

In recent years, non-Hermitian (NH) quantum systems have been actively studied [1,2]. However, since most of the previous studies dealt with single-particle physics, understanding of many-body physics in NH systems is yet in its infancy.
Motivated by recent experimental advances in ultracold fermionic atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with complex-valued interactions arising from inelastic scattering between fermions [3]. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are similar to but different from the standard BCS ones because of the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: the superfluidity breaks down and reappears with increasing dissipation, featuring exceptional points for weak attractive interactions. As 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.
[1] Y. Ashida et al., Nature Commun. 8, 15791 (2017).
[2] M. Nakagawa et al, Phys. Rev. Lett. 121, 203001 (2018).
[3] K. Yamamoto et al., Phys. Rev. Lett.
123, 123601 (2019).