  We propose a quantum interference cooling scheme for a nano-mechanical
resonator (NAMR) in a hybrid optomechanical system, where the atoms are trapped
in an optomechanical cavity, coupling to an additional optical cavity. The
absorption of the optomechanical resonator can be modified by quantum
interference effects induced by the atom-cavity and cavity-cavity couplings
independently. With the employment of the quantum interference, the desired
transition for cooling is enhanced, along with the heating suppression due to
the undesired transition. As a result, the NAMR vibration can be cooled down to
its ground state. Particularly, with the assistance of the atoms, our scheme is
experimentally feasible even for lower qualities cavities, which much reduces
the experimental difficulty.
