Hybrid exceptional point and its dynamical encircling in a two-state system

Hybrid exceptional points (HEPs) are non-Hermitian degeneracies that exhibit different dispersion relations (e.g., linear or square-root) along different directions in the parameter space. Here, we show that a two-state system consisting of coupled ferromagnetic waveguides applied with a bias magnetic field can support the presence of a HEP. A configuration is designed to dynamically encircle the HEP, showing a nonchiral behavior due to the unique topological structure of energy surfaces around the HEP. This is in contrast to the chiral dynamics found when an exceptional point is encircled dynamically. We performed numerical simulations and microwave experiments to demonstrate the topological transition enabled by the HEP in the proposed system.