  We investigate a hybrid quantum system consisting of a cavity optomechanical
device optically coupled to an ultracold quantum gas. We show that the
dispersive properties of the ultracold gas can be used to dramatically modify
the optomechanical response of the mechanical resonator. We examine hybrid
schemes wherein the mechanical resonator is coupled either to the motional or
the spin degrees of freedom of the ultracold gas. In either case, we find an
enhancement of more than two orders of magnitude in optomechanical cooling due
to this hybrid interaction. Significantly, based on demonstrated parameters for
the cavity optomechanical device, we identify regimes that enable the ground
state cooling of the resonator from room temperature. In addition, the hybrid
system considered here represents a powerful interface for the use of an
ultracold quantum gas for state preparation, sensing and quantum manipulation
of a mesoscopic mechanical resonator.
