Encircling exceptional points in non-Hermitian systems with quasidegenerate energy levels

Dynamically encircling an exceptional point in non-Hermitian systems shows a chiral state switching behavior as a result of the nonadiabatic transition between nonorthogonal eigenstates. It has been revealed that the chiral dynamics is protected by the topological structure of eigenvalue sheets where only one lowest-loss sheet exists. This raises the question on what the dynamics would be in non-Hermitian systems possessing multiple degenerate lowest-loss energy levels. Here, we address this question by studying a photonic-waveguide-array non-Hermitian system where two exceptional points are encircled dynamically. The system possesses four quasidegenerate lowest-loss eigenvalue sheets and such topological structure results in an exotic nonchiral behavior for switching eigenstates such that the final state is always a superposition of the four lowest-loss eigenstates. We find that this intriguing phenomenon is robust to a certain perturbation of the system parameters. Our findings enrich the understanding of exceptional point-encirclement physics and may inspire potential non-Hermitian applications for manipulating waves.