Back-action ground state cooling of a micromechanical membrane via intensity-dependent interaction

We propose a theoretical scheme to show the possibility of achieving the quantum ground state cooling of a vibrating micromechanical membrane inside a high finesse optical cavity by back-action cooling approach. The scheme is based on an intensity-dependent coupling of the membrane to the intracavity radiation pressure field. We find the exact expression for the position and momentum variances of the membrane by solving the linearized quantum Langevin equations in the steady-state, conditioned by the Routh-Hurwitz criterion. We show that by varying the Lamb-Dicke parameter and the membrane's reflectivity one can effectively control the mean number of excitations of vibration of the membrane and also cool down the system to micro-Kelvin temperatures.