  We investigate a hybrid optomechanical system in which a membrane oscillator
is coupled to a collective spin of ground states of an intracavity
$\Lambda$-type three-level atomic medium. The cavity field response is greatly
modified by atomic coherence and the anomalous dispersion generated by two
Raman pumping beams near two-photon resonance. The optomechanical interaction,
therefore radiation pressure force, is substantially enhanced due to
superluminal propagation of photons in the cavity. Such improvement facilitates
ground-state cooling of the mechanical oscillator with room temperature thermal
environment. Moreover, it can greatly improve the sensitivity and bandwidth of
displacement measurement. In such system, optically-controlled strong-coupling
interaction between the mechanical oscillator and cavity field could be
implemented on small intracavity photon number, even at the single quanta
level, which is important for weak-light nonlinear photonics and the generation
of nonclassical quantum states in the mechanical field.
