Enhanced Phonon Blockade in a Weakly Coupled Hybrid System via Mechanical Parametric Amplification

We propose how to achieve strong phonon blockade (PB) in a hybrid spin-mechanical system in the weak-coupling regime. We demonstrate the implementation of magnetically induced two-phonon interactions between a mechanical cantilever resonator and an embedded nitrogen-vacancy center, which, when combined with parametric amplification of the mechanical motion, produces significantly enlarged anharmonicity in the eigenenergy spectrum. In the weak-driving regime, we show that strong PB appears in the hybrid system along with a large mean phonon number, even in the presence of strong mechanical dissipation. We also show flexible tunability of phonon statistics by controlling the strength of mechanical parametric amplification. Our work opens up prospects for the implementation of an efficient single-phonon source, with potential applications in quantum phononics and phononic quantum networks.