Nonlinear dynamics of an optomechanical system with a coherent mechanical pump: Second-order sideband generation

Second-order sideband generation in a coherent-mechanical pumped optomechanical system is discussed, and the features of the coherent mechanical pump induced enhancement of second-order sideband generation are identified. We show that the coherent mechanical pump induced enhancement of second-order sideband generation exhibits an essential difference between the case of a weak control field and a strong control field. In the weak control field case, the efficiency of second-order sideband generation increases as the amplitude of the mechanical pump increases. In the strong control field case, the effect of optomechanically induced transparency occurs and increasing the amplitude of the mechanical pump does not always bring an enhancement of second-order sideband generation. The phase-dependent effect of the second-order sideband generation with a coherent mechanical pump is also discussed, and it is shown that the phase difference $\ensuremath{\phi}$ plays an important role in the process of second-order sideband generation.