Strong tunable spin-spin interaction in a weakly coupled nitrogen vacancy spin-cavity electromechanical system

The long coherence time of a single nitrogen vacancy (NV) center spin in\ndiamond is a crucial advantage for implementing quantum information processing.\nHowever, the realization of strong coupling between single NV spins is\nchallenging. Here we propose a method to greatly enchance the interaction\nbetween two single NV spins in diamond which are only weakly coupled to an\nelectromechanical cavity. Owing to the presence of a critical point for the\nlinearized electromechanical subsystem, the coupling between a single NV spin\nand the high-frequency polariton (formed by the mechanical and cavity modes)\ncan be fully decoupled, but the coupling between the single NV spin and the\nlow-frequency polariton is however greatly enhanced. Thus, AC Stark shift of\nthe single NV spin can be measured. With the low-frequency polariton as a\nquantum bus, a strong coupling between two single NV centers is achievable.\nThis effective strong coupling can ensure coherent quantum-information exchange\nbetween two spin qubits in the weakly coupled spin-cavity elecromechanical\nsystem.\n