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We propose and analyze a novel mechanism for long-range spin-spininteractions in diamond nanostructures. The interactions between electronicspins, associated with nitrogen-vacancy centers in diamond, are mediated bytheir coupling via strain to the vibrational mode of a diamond mechanicalnanoresonator. This coupling results in phonon-mediated effective spin-spininteractions that can be used to generate squeezed states of a spin ensemble.We show that spin dephasing and relaxation can be largely suppressed, allowingfor substantial spin squeezing under realistic experimental conditions. Ourapproach has implications for spin-ensemble magnetometry, as well asphonon-mediated quantum information processing with spin qubits.

Phonon-induced spin-spin interactions in diamond nanostructures: application to spin squeezing