Second-order magnetic field gradient-induced strong coupling between nitrogen-vacancy centers and a mechanical oscillator

We consider a cantilever mechanical oscillator (MO) made of diamond. A nitrogen-vacancy (NV) center lies at the end of the cantilever. Two magnetic tips near the NV center induce a strong second-order magnetic field gradient. Under coherent driving of the MO, we find that the coupling between the MO and the NV center is greatly enhanced. We studied how to generate entanglement between the MO and the NV center and realize quantum state transfer between them. We also propose a scheme to generate two-mode squeezing between different MO modes by coupling them to the same NV center. The decoherence and dissipation effects for both the MO and the NV center are numerically calculated using the present parameter values of the experimental configuration. We have achieved high fidelity for entanglement generation, quantum state transfer, and large two-mode squeezing.