Photon–phonon entanglement and spin squeezing via dynamically strain-mediated Kerr nonlinearity in dressed nitrogen–vacancy centers

We propose a scheme to generate photon–phonon entanglement and spin squeezing in a hybrid system which is composed of the nitrogen–vacancy (NV) centers, nanomechanical resonator (NMR), and optical cavity. The triplet ground states of the NV centers which have been embedded in the middle of the clamped–clamped NMR are dressed by two strong microwave fields. Kerr nonlinearity is established by an applied microwave field and the vibrational modes of NMR coupling to the dressed-state transitions. The quantum correlations of the applied microwave field, vibrational mode, and NV centers are realized based on the parametric down-conversion-like and beam-splitter-like interactions in the hybrid system, which generate the photon–phonon entanglement and spin squeezing. In this nonlinear processes, the dynamically mediated strain of NMR, as a nonlinear switch, plays the central role in the establishment of such quantum correlations. Our scheme can be applied to quantum nondemolition measurement, quantum sensing, and quantum metrology.