We study a setup where a single negatively-charged silicon-vacancy center indiamond is magnetically coupled to a low-frequency mechanical bending mode andvia strain to the high-frequency phonon continuum of a semi-clamped diamondbeam. We show that under appropriate microwave driving conditions, this setupcan be used to induce a laser cooling like effect for the low-frequencymechanical vibrations, where the high-frequency longitudinal compression modesof the beam serve as an intrinsic low-temperature reservoir. We evaluate theexperimental conditions under which cooling close to the quantum ground statecan be achieved and describe an extended scheme for the preparation of astationary entangled state between two mechanical modes. By relying onintrinsic properties of the mechanical beam only, this approach offers aninteresting alternative for quantum manipulation schemes of mechanical systems,where otherwise efficient optomechanical interactions are not available.
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