Proximity-encirclement of exceptional points in a multimode optomechanical system

Abstract

Dynamic encirclement of second-order exceptional points (EPs) exhibits chiral state transfer; however, investigations into the dynamics involving multiple and higher-order EPs remain sparse. Here, we study the proximity-encirclement of EPs within a multimode optomechanical system to elucidate the closed-path evolution in high-order non-Hermitian systems. Our optomechanical framework presents three distinct EP scenarios: absence of EPs, presence of a pair of second-order EPs, and the existence of a third-order EP. We meticulously analyze the system’s dynamic behavior, considering variables such as initial state, loop orientation and velocity, loop starting point variance, and the number and order of encircled EPs during state transfer processes. The findings reveal that chiral or non-reciprocal state transfer can be achieved when a loop encircles a second-order EP with varying radii. Encircling two second-order EPs results exclusively in chiral state transfer. Furthermore, both chiral and non-reciprocal state transfers are observed within a single loop encircling a third-order EP. These phenomena in the context of multimode optomechanical systems provide a new approach for manipulating state transfer in higher-order non-Hermitian systems.