Enhanced four-wave mixing in P T-symmetric optomechanical systems

We investigate the enhanced four-wave mixing (FWM) process in a parity-time (P T)-symmetric optomechanical system, where an active cavity is coupled to a passive cavity supporting a mechanical mode. The passive cavity is optically driven by a strong control field and a weak probe field, and the mechanical mode is excited by a weak coherent driving field. By tuning the coupling strength between the two cavities with balanced gain and loss, we find that the FWM intensity can be significantly enhanced near the exceptional points (EPs) at low control power, which is about 12 orders of magnitude higher than that of the single-cavity case. Due to the interference effect induced by the optical and mechanical driving field, it is shown that the FWM intensity can be further enhanced or suppressed by tuning the amplitude and phase of the mechanical driving field. Moreover, the dependence of the FWM intensity on the frequency and power of the control field is also discussed. Our work provides a route to enhance the four-wave mixing process in a flexible way.