Non-Hermitian Effects in Dicke models

The Dicke model, which describes the collective interaction between an ensemble of atoms and a single-mode photon field, serves as a fundamental framework for studying light-matter interactions and quantum electrodynamic phenomena. In this work, we investigate the manifestation of non-Hermitian effects in a generalized Dicke model, where two dissipative atom ensembles interact with a single-mode photon field. By applying the Holstein-Primakoff transformation, we explore the system in the semiclassical limit as a non-Hermitian Dicke model, revealing rich exceptional points (EPs) and diabolic points in such a system. We find that, by introducing the nonlinear saturation gain into an atomic ensemble, higher-order EP can be induced, leading to intriguing properties. Furthermore, if the system is extended to a one-dimensional chain, then the band topology will interplay with the non-Hermitian effect. In the quantum regime, we explore the quantum signature of EPs, noting that the conditions for their emergence are influenced by discrete photon numbers. We further study the transition from photon anti-bunching to bunching at a steady state, driven by non-Hermitian dynamics. Our findings deepen the understanding of non-Hermitian physics in light-matter interaction which is instructive for the design of advanced photonic and quantum systems.