Controllable optical-sideband generation and synchronization in a mechanical gain-loss optomechanical system

The interaction between light and mechanical vibrations in a cavity is often exploited to produce higher-order sidebands (HOSs) or combs, which are used in optical communication networks and spectroscopy, among other things. Although an extensive study of optomechanically induced HOSs has been done, their proper control and manipulation using only continuous-wave (cw) laser drive are still to be explored. Here, we employ a mechanical parity-time-($\mathcal{PT}$) symmetric structure with optically induced gain and loss. It allows us to manipulate the flow of mechanical energies between the cavities, which has consequences on the optical response of the cavities. Based on our numerical investigations, we find that the higher-order optical sidebands start to emerge if $\mathcal{PT}$ symmetry is broken. We precisely control the number of higher-order sideband lines by adjusting the coupling rate between the cavities with fixed drive power. In addition, we observe that the exceptional point (EP) induces the formation of two synchronized higher-order optical-sideband spectra, which opens a promising EP-based platform for the realization of optical readout of various mechanical synchronization phenomena, copies of the optomechanical frequency comb, sensing, and synchronization of remote clock time, among other things.