The optomechanics can generate fantastic effects of optics due to appropriate mechanical control.Here we theoretically study effects of slow and fast lights in a single-sided optomechanical cavity with an external force. The force-induced transparency of slow/fast light and the force-dependent conversion between the slow and fast lights are resulted from effects of the rotating-wave approximation (RWA) and the anti-RWA, which can be controlled by properly modifying the effective cavity frequency due to the external force. These force-induced phenomena can be applied to control of the light group velocity and detection of the force variation, which are feasible using current laboratory techniques.

We propose a quantum interference cooling scheme for a nano-mechanical resonator (NAMR) in a hybrid optomechanical system. In our scheme, atoms are trapped in an optomechanical cavity, and this optomechanical cavity interacts both atoms and an optical cavity. Therefore, the absorption of the optomechanical resonator can be modified by quantum interference effects induced by the atom-cavity and cavity-cavity couplings. With the modification of the quantum interference, the desired transition for cooling is enhanced, while the undesired transition for heating can be suppressed. As a result, the NAMR vibration can be cooled down to its ground state. Particularly, with the assistance of the atoms, the experimental difficulty can be reduced since the effective decay rate of the cavity can be decreased via the quantum interference for the atom-cavity coupling.

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