Third-order natural Non-Hermitian quantization of quad-photon Rabi oscillation in an atomic ensemble

A natural non– Hermitian system is constructed based on 85Rb atoms and multi-dressing fields. On this basis, the influence of different dressing fields on symmetry breaking and energy level degeneracy during four-photon spontaneous eight-wave mixing based on seventh-order nonlinear effects is investigated, and four-photon correlations are analyzed. When the dressing Rabi frequency dominates, the real part splits, leading to in phase constructive dressing, its symmetry breaking is localized, non-degenerate, Abelian and has low symmetry. When the dephase rate dominates, the imaginary part splits, leading to out-of-phase destructive dressing, its symmetry breaking is nonlocal, degenerate, non– Abelian and highly symmetric. The interactions between the dressing fields and the eigenvalue splitting modes of two double dressing effects that have third-order EPs are compared, and the role of the internal and external dressing fields in the formation of third-order EPs is clarified. The third-order non-Hermitian interaction between two dressing fields of the nested scheme is strongest and weakest for the parallel scheme, with the cascade scheme intermediate between them. This study is of value for the detection and quantum storage of quantum states.