Dynamic of time-independent and time-dependent asymmetric Gross-Pitaevskii equation around exceptional point

Systems operating at exceptional points (EPs) are highly sensitive to small perturbations, making it challenging to work near an EP. Eigenvalue analysis of the Gross-Pitaevskii equation has shown that asymmetric nonlinearity can compensate for detuning effects. However, an experimentally feasible system based on asymmetric nonlinear coupled resonators has not yet been explored. Additionally, some intriguing features of such a system are hidden in time domain analysis, which is rarely investigated. In this study, we demonstrate this feature using a full-wave simulation of an asymmetric nonlinear coupled resonator based on the finite-element method in Comsol. The time-dependent analysis reveals that detuning can shift the system from PT-symmetric to broken PT-symmetric (or vice versa), and nonlinearity can reverse this dynamic. This study provides an experimental framework for examining exceptional points (EPs) in nonlinear detuned coupled resonators and opens up new avenues for fundamental research into the influence of nonlinearity and detuning on the system’s state during EP encirclement.