  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.
