Quantum-state transfer between a Bose-Einstein condensate and an optomechanical mirror

We describe a scheme that allows for the transfer of a quantum state between a trapped atomic Bose condensate and an optomechanical end mirror mediated by a cavity field. Coupling between the mirror and the cold gas arises from the fact that the cavity field can produce density oscillations in the gas which in turn acts as an internal Bragg mirror for the field. After adiabatic elimination of the cavity field we find that the coherent dynamics of the atomic condensate-mirror hybrid system is described by an effective state transfer beam-splitter Hamiltonian. The state transfer fidelity is limited principally by the quantum noise associated with the intracavity field.