Dynamic Cooling of a Micromechanical Membrane in a Double-cavity Optomechanical System

We theoretically present an optomechanical cooling scheme of a double optical modes which are coupled with the same mechanical resonator by the radiation pressure to analyze the dynamical cooling of a micromechanical membrane. The mean value of the total second-order moments are obtained by solving linearized quantum Langevin equations. We discuss the effect of the significant parameters of the system on the instantaneous-state mean phonon number of the oscillator cooled to the ground state under the resolved sideband regime. Furthermore, the steady-state cooling limit is also studied and the results show that the final mean phonon number splits into two minimum values when the detunings of the two cavity modes are different. Moreover, the minimal value of the final mean phonon number is much less than the case of equal driving detuning. By regulating the detunings of the optical modes from the corresponding driving fields and increasing the coupling strengths, the cooling effect will be optimized obviously.