We present a cavity dissipation scheme to prepare a hybrid system of an atomic ensemble and a moving mirror in squeezed and entangled states. This scheme is based on four-wave mixing in the atoms and radiation pressure on the mirror, both of which combine to lead to Bogoliubov interactions of the atoms and the mirror with the cavity fields. Under adiabatic conditions, the cavity fields cause the hybrid Bogoliubov modes to evolve into the vacuum states, which correspond to the two-mode squeezed and entangled states. The dependence of the hybrid entanglement on the system p...
