We investigate the multistability of exciton-polariton condensates excited by a nonresonant pump. An increase in pumping power moves the system away from non-Hermitian spectral degeneracy towards spectrum splitting through an exceptional point, which induces a transition from monostability to multistability. 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 to steady states. A steady state with multi-peak soliton different from general single-peak soliton is discovered for attractive polariton-polariton interaction. Moreover, we depict the diagram of the multistability in full parameter space to accurately manipulate the multistability. Our results open up exciting possibilities for controlling non-Hermitian quantum multistable states, which may be useful to designing polariton-based devices exploiting optical multistability.
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