  We propose a technique aimed at cooling a harmonically oscillating mirror
mechanically coupled to another vibrating mirror to its quantum mechanical
ground state. Our method involves optmechanical coupling between two optical
cavities. We show that the cooling can be controlled by the mechanical coupling
strength between the two movable mirrors, the phase difference between the
mechanical modes of the two oscillating mirrors and the photon number in each
cavity. We also show that both mechanical and optical cooling can be achieved
by transferring energy from one cavity to the other. We also analyze the
occurrence of normal-mode splitting (NMS). We find that a hybridization of the
two oscillating mirrors with the fluctuations of the two driving optical fields
occurs and leads to a splitting of the mechanical and optical fluctuation
spectra.
