Higher-Order Exceptional Points Induced by Non-Markovian Environments

Abstract

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. Furthermore, we show that these non-Markovianity-induced higher-order EPs admit a topological characterization as defects in the relevant pseudo-Hermitian parameter space, with quantized charges described by resultant winding numbers. 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 note that the non-Markovian mechanism for generating higher-order EPs is not restricted to pseudo-Hermitian systems, but can be extended to generic non-Hermitian quantum systems. Additionally, possible experimental implementations based on superconducting circuits are also discussed.

21 pages, 7 figures, 2 table. This updated version is essentially identical to the version published in Laser & Photonics Reviews