Tunable optical-gain-induced chaotic dynamics in a hidden PT -symmetric optomechanical system

Exceptional points (EPs) are the singular branch points of the non-Hermitian Hamiltonian spectrum. They lead to many exotic phenomena of non-Hermitian systems. However, it is hard to realize parity-time $(\mathcal{PT})$ symmetry breaking at EPs by increasing the optical gain due to the limitation of the optical gain materials. Here we propose a scheme to realize gain-induced $\mathcal{PT}$ symmetry breaking in two coupled passive optical resonators with a Stokes gain in the optomechanical resonator. As the Stokes gain results from radiation pressure coupling, it depends on the strength of the pump field. For this reason, $\mathcal{PT}$ symmetry breaking can be triggered by increasing the strength of the pump field. Moreover, Stokes gain also relies on the effective detuning of optomechanics, which is linear to the photon number. Therefore, $\mathcal{PT}$ symmetry breaking can also be induced by increasing the coupling strength between two coupled resonators and thus decreasing the photon number of the optomechanical resonator. In addition, this work opens up a method to control hidden $\mathcal{PT}$ symmetry breaking and nonlinear dynamics with radiation pressure coupling.