Tunable Two-Axis Twist Interaction of Multiple Spins Using Two-Phonon Drive in a Spin-Mechanical System

Spin-spin interactions play an important role in quantum computing and quantum metrology. Here a simple scheme is proposed to control the induced spin-spin interactions in a spin-mechanical hybrid system, where a tunable two-phonon drive without a complex nonlinear process can be easily acquired. In this scheme, the nitrogen-vacancy (NV) centers are coupled to a mechanical cantilever through either magnetic gradient or strain coupling. Through modulating the spring constant of the mechanical cantilever with a time-dependent pump, an intrinsic nonlinear drive can be acquired and the interaction of the NV spins can be easily controlled using the adjustable two-axis twist (TAT) Hamiltonian. This proposal needs neither additional nonlinear resources nor optical pumping and driving of multi-level atoms, which tremendously facilitates the experimental realization of this scheme. Then, the TAT Hamiltonian is used to achieve the Heisenberg-limited spin squeezing. The considered dissipations will not interfere the generation of squeezed spin states. Besides, it is found that the spin squeezing is robust against the variation of the parameters in the system. This scheme can make it feasible to generate the interaction between spins in solid-state spin-phonon systems.