Magnetically Induced Two-Phonon Blockade in a Hybrid Spin-Mechanical System

Phonon blockade is an important quantum effect for revealing the quantum behaviors of mechanical systems. For a nitrogen-vacancy center spin strongly coupled to a mechanical resonator via the second-order magnetic gradient, we show that the qubit driving can lead to the implementation of the two-phonon blockade, while the usual mechanical driving only allows for the appearance of a single-phonon blockade. As a signature, we investigate three-phonon antibunching with a simultaneous two-phonon bunching process by numerically calculating the second-order and third-order correlation functions. We also analyze in detail the influence of the system parameters (including the qubit driving strength, the dephasing rate of the qubit, as well as the thermal phonon number) on the quality of the two-phonon blockade effect. Our work provides an alternative method for extending the concept of a phonon blockade from a single phonon to multiphonon. It is of direct relevance for the engineering of multiphonon quantum coherent devices and thus has potential applications in quantum information processing.