Selective Chiral Multistate Switching via the Dynamic Interplay of Diabolic and Exceptional Points

Non-Hermitian systems give rise to nontrivial phenomena due to their ability to exhibit peculiar spectral singularities known as exceptional points. Especially, the dynamical encirclement of exceptional points in a system parameter space enables chiral state switching. Although this chiral behavior can be effectively controlled in two-mode structures, extending such control to higher-dimensional systems with multiple exceptional points presents significant challenges, particularly when aiming to steer the system toward a specific target state, a capability crucial for advancing such fields as optical communication and quantum information processing. In this work, we overcome this challenge by experimentally demonstrating a genuine programmable symmetric-asymmetric multistate switching in a four-mode optical system. This is achieved through the controlled dynamic interplay between exceptional and diabolic points in the Hamiltonian spectrum. Our results lay the groundwork for the practical development of advanced light manipulation protocols in multimode photonic setups.