Using interference for high fidelity quantum state transfer in optomechanics

We present a theoretical study of a two-cavity optomechanical system (e.g. a single mechanical resonator coupled to both a microwave and an optical cavity), investigating how interference can be used to perform mechanically-mediated quantum state transfer between the two cavities. We show that this optomechanical system possesses an effective ``mechanically-dark'' mode which is immune to mechanical dissipation; utilizing this feature allows highly efficient transfer of intra-cavity states, as well as of itinerant photon states. Simple analytic expressions for the fidelity of transferring both Gaussian and non-Gaussian states are provided. Our work has relevance to ongoing experimental efforts in quantum optomechanics (e.g., C.~A.~Regal and K.~W.~Lehnert, J. Phys.: Conf. Ser. 264, 012025 (2011); A.~H.~Safavi-Naeini and O.~Painter, New J. Phys. 13, 013017 (2011)).