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We propose and investigate a hybrid optomechanical system consisting of amicro-mechanical oscillator coupled to the internal states of a distantensemble of atoms. The interaction between the systems is mediated by a lightfield which allows to couple the two systems in a modular way over longdistances. Coupling to internal degrees of freedom of atoms opens up thepossibility to employ high-frequency mechanical resonators in the MHz to GHzregime, such as optomechanical crystal structures, and to benefit from the richtoolbox of quantum control over internal atomic states. Previous schemesinvolving atomic motional states are rather limited in both of these aspects.We derive a full quantum model for the effective coupling including the mainsources of decoherence. As an application we show that sympathetic ground-statecooling and strong coupling between the two systems is possible.

Long Distance Coupling of a Quantum Mechanical Oscillator to the Internal States of an Atomic Ensemble