  We investigate theoretically the effect of optical feedback from a cavity
containing an ultracold two level atomic ensemble, on the bistable behavior
shown by mean intracavity optical field and the ground state cooling effect of
the mechanical oscillator in an optomechanical cavity resonator. The optical
bistability can be controlled by tuning the frequency and power of the single
driving laser as well as by varying the atom-cavity coupling strength in the
atomic cavity. Study of the cooling of the mechanical oscillator, in both good
and bad cavity limits, reveals that the hybrid system is more efficient in
cooling in comparison to a generic optomechanical setup, even at room
temperature. In essence, our work emphasizes the impact of the coupling with
the atomic cavity on the radiation pressure effects in the optomechanical
cavity.
