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 nondiagonalizable 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.
Recently, the influence of dissipation on a quantum system has attracted much attention, particularly on how the non-Hermitian terms modify the energy spectrum, band topology, and phase transition point. Motivated by the recent investigation of non-Hermitian
s-wave superfluidity, we study the non-Hermitian chiral
p+ip superfluid (SF) with a complex-valued interaction, originating from inelastic scattering between fermions. We reformulate the non-Hermitian mean-field theory for chiral SFs and derive the gap equation in the path integral approach. By numerically solving the gap equation, we obtain the phase diagram of the non-Hermitian
p+ip SF, characterized by the reentrant SF transition and dissipation-induced SF phase, as a result of the evolution of the exceptional lines. The method can be extended to higher partial-wave chiral SFs, such as
d+id and
f+if-wave SFs. We further consider such a chiral
p+ip SF on a square lattice, to investigate the influence of dissipation on topology. We find that the non-Hermitian skin effect is absent in the specific cylinder geometry, in which the topology associated with the edge modes and Chern number is robust to dissipation. Besides, we find that the energies at the robust point nodes and line nodes are pure real. We further verify the conditions of zero winding number in (quasi-) one-dimensional systems, and prove an associated ``no-go'' theorem, which is hopefully applied to explore the geometry dependent skin effect.
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.
We investigate the non-Hermitian (NH) attractive Fermi-Hubbard model with asymmetric hopping and complex-valued interactions, which can be realized by collective one-body loss and two-body loss. By means of the NH BCS theory, we find that the weak asymmetry of the hopping does not affect the BCS superfluidity since it only affects the imaginary part of the eigenvalues of the BdG Hamiltonian. Systematic analysis in the
d-dimensional hypercubic lattices clarifies that the singularity in the density of states affects the phase boundary between the normal and dissipation-induced superfluid states. Our results can be tested in ultracold atoms by using the photoassociation techniques and a nonlocal Rabi coupling with local losses and postselecting null measurement outcomes with the use of the quantum-gas microscope.
Having both elastic and inelastic two-body processes that are characterized by a complex
s-wave scattering length between $\ensuremath{\uparrow}$ and $\ensuremath{\downarrow}$ fermions in mind, here we apply the non-Hermitian extension of the mean-field theory to the BCS-BEC evolution at zero temperature. We construct the phase diagram of the system, where we find a reentrant superfluid (SF) transition that is intervened by a normal and/or a metastable phase as a function of increasing inelasticity. This transition occurs in a large parameter regime away from the unitarity, i.e., on both the BCS and BEC sides of the resonance, and it is mostly governed by the exceptional points. In addition, except for the strongly inelastic regime, we also show that the SF phase can be well described by the condensation of weakly interacting bosonic pairs in the two-body bound state with a complex binding energy.
We study non-Hermitian (NH) fermionic superfluidity subject to dissipation of Cooper pairs on a honeycomb lattice, for which we analyze the attractive Hubbard model with a complex-valued interaction. Remarkably, we demonstrate the emergence of the dissipation-induced superfluid phase that is anomalously enlarged by a cusp on the phase boundary. We find that this unconventional phase transition originates from the interplay between exceptional lines and Van Hove singularity, which has no counterpart in equilibrium. Moreover, we demonstrate that the infinitesimal dissipation induces the nontrivial superfluid solution at the critical point. Our results can be tested in ultracold atoms with photoassociation techniques by postselecting special measurement outcomes with the use of quantum-gas microscopy, and they can lead to an understanding of the NH many-body physics triggered by exceptional manifolds in open quantum systems.
Abstract We theoretically explore a non-Hermitian superfluid model with complex-valued interaction, inspired by two-body loss stemming from inelastic scattering observed in ultracold atomic experiments. Utilizing both the right-eigenstate-based mean-field theory and its biorthogonal counterpart, we study the properties of the system. Notably, the right-eigenstate-based framework produces smooth and continuous solutions, in stark contrast to the absence of nontrivial solutions and the abrupt discontinuities observed in the biorthogonal-eigenstate-based framework under moderate dissipation. In addition, the lower condensation energy obtained in the former framework suggests its superior suitability for describing this system. Furthermore, we explore the impact of backscattering, a crucial factor in realistic systems. Our analysis reveals that, facilitated by two-body loss, even moderate backscattering destabilizes the superfluid state. Sufficiently strong backscattering completely destroys it, highlighting a key mechanism for the fragility of this non-Hermitian quantum phase.