Non-Hermitian spectrum and multistability in exciton-polariton condensates

We investigate non-Hermitian spectrum and multistability of exciton-polariton condensates excited by a nonresonant pump. An increase in pumping power moves the system away from non-Hermitian spectrum degeneracy toward bifurcation through an exceptional point, which induces a transition from monostability to multistability. The spectrum can be used as a universal method for detecting this transition. In the region of multistability, the system contains one steady and two metastable states. The analyses of stability show that metastable states maintain a finite lifetime and eventually evolve into steady states, which are induced by non-Hermitian skin effects. We also discover a steady state with multipeak soliton for attractive polariton-polariton interaction, which is different from general single-peak soliton for repulsive interaction. Our results open up exciting possibilities for controlling non-Hermitian quantum multistable states, which may be useful for designing polariton-based devices exploiting optical multistability.