The second-order sideband enhancement in spinning resonators with an external phonon pump

We theoretically investigate the properties of the second-order sideband generation in a spinning optomechanical system driven by a phonon pump. When the driving frequency of the phonon pump is equal to the detuning of probe fields, the second-order sideband generation efficiency can be easily modified by tuning the amplitude, phase of the phonon pump, and the rotation speed of the resonator. As the amplitude of the phonon field increases, the second-order sideband efficiency is significantly enhanced if the driving fields come from the left side. Furthermore, we discuss the phase-dependent effect of the phonon pump on generating the second-order sideband and demonstrate that the second-order sideband generation process can be flexibly adjusted by the initial phase. Finally, we study the influence of pump power on second-order sideband and indicate that the remarkable efficiency of second-order sideband can be obtained at a very small pump power by adding a phonon field. Our results may have potential applications for modulating the nonlinear optical properties in optical cavities.