Robust Four-Wave Mixing and Double Second-Order Optomechanically Induced Transparency Sideband in a Hybrid Optomechanical System

We theoretically research the four-wave mixing (FWM) and second-order sideband generation (SSG) in a hybrid optomechanical system under condition of pump on-resonance off-resonance, where an resonator is coupled to another nanomechanical (NR) via Coulomb interaction. Using standard quantum optics method input–output theory, we obtain analytical solution FWM SSG with strict derivation. According numerical simulations, find that can be controlled regulating coupling strength frequency difference two NRs different detuning, which also gives means determine NRs. Furthermore, sensitive shows double optomechanically induced transparency (OMIT) sidebands controlling frequencies resonators. Our investigation may increase comprehension nonlinear phenomena optomechanics systems.