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Exceptional points (EPs) have recently attracted considerable attention inthe study of non-Hermitian systems and in applications such as sensors and modeswitching. In particular, nontrivial topological structures of EPs have beenstudied intensively in relation to encircling EPs. Thus, EP generation iscurrently an important issue in several fields. To generate multiple EPs,multiple levels or composite physical systems have been employed with Hermitiancouplings. In this study, we generate multiple EPs on two-level systems in asingle microcavity by adopting the non-Hermitian coupling of a non-HermitianHamiltonian under the imaginary (dominant) coupling. The topological structuresof Riemann surfaces generated by non-Hermitian coupling exhibit features thatare different from those of Riemann surfaces generated by Hermitian coupling.The features of these topological structures of Riemann surfaces were verifiedby encircling multiple EPs and using a Riemann sphere.

Double exceptional points generated by the strong imaginary coupling of a non-Hermitian Hamiltonian in an optical microcavity