  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.
