Tunable fast to slow light and second-order sideband generation in an optomechanical system with phonon pump

We theoretically demonstrate optomechanically induced transparency (OMIT) and its related coherent optical propagation properties such as fast and slow light effects in a cavity optomechanical system driven by a weak coherent phonon pump for suitable parametric and detuning regimes. The probe transmission spectrum experiences different processes under different detuning regimes, and the numerical simulations indicating a tunable and controllable fast-to-slow light propagation can be achieved by controlling the driving amplitudes and phase of the phonon pump. Further, the second-order sideband (SOS) generation is also demonstrated in the system, and it is found that the efficiency of the SOS generation can be significantly enhanced with manipulating the phonon pump in the resonance regime with numerical simulations. More interestingly, the SOS generation is also sensitive to the detuning (the off-resonance regime), and a robust SOS can be induced and the efficiency of the SOS generation even presents mode splitting which is similar to the linear OMIT. These results lead to good tunability of SOS generation and may find applications in manipulation of light propagation