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Higher-order Exceptional Points Induced by Non-Markovian Environments

Exceptional points (EPs) are central to non-Hermitian physics because of their unique properties and broad application prospects. While extensively studied in parity-time ($\mathcal{P}\mathcal{T}$)-symmetric systems and under Markovian dynamics, their exploration in broader pseudo-Hermitian settings, particularly in those involving non-Markovian environments, remains largely unexplored. In this study, we investigate a pseudo-Hermitian system consisting of three coupled optical cavities interacting with non-Markovian environments. Compared to the Markovian baseline, we demonstrate that the emergence of non-Markovian memory effects enlarges the dimensionality of the parameter space of the system, thereby giving rise to higher-order EPs. Moreover, we observe that the pseudo-Hermitian system with an effective gain induced by coherent perfect absorption enables the higher-order EPs to be directly read out from the output spectrum. We also find that breaking the symmetry of the parameter space of the system reduces the order of the EPs. Furthermore, we note that the non-Markovian mechanism for generating higher-order EPs extends beyond pseudo-Hermitian systems to generic non-Hermitian quantum systems. Additionally, possible experimental implementations based on a superconducting circuit are also discussed. Our findings reveal how non-Markovianity enhances the sensitivity of the system and provide a theoretical insight into the experimental observation of higher-order EPs.