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

Exceptional points (EPs) have recently attracted considerable attention in the study of non-Hermitian systems and in applications such as sensors and mode switching. In particular, nontrivial topological structures of EPs have been studied intensively in relation to encircling EPs. Thus, EP generation is currently an important issue in several fields. To generate multiple EPs, multiple levels or composite physical systems have been employed with Hermitian couplings. In this study, we generate multiple EPs on two-level systems in a single microcavity by adopting the non-Hermitian coupling of a non-Hermitian Hamiltonian under the imaginary (dominant) coupling. The topological structures of Riemann surfaces generated by non-Hermitian coupling exhibit features that are different from those of Riemann surfaces generated by Hermitian coupling. The features of these topological structures of Riemann surfaces were verified by encircling multiple EPs and using a Riemann sphere.