Phonon blockade in a quadratically coupled optomechanical system with two-phonon driving

We propose a scheme to enhance phonon blockade effect in a quadratically coupled optomechanical system. By applying a degenerate parametric drive to the mechanical oscillator, we introduce a mechanical parametric amplifier (MPA) to the system. We show that the phonon blockade can be achieved in both the single-phonon resonant regime and multipath interference regime due to the optomechanical nonlinearity and MPA. By combining the two regimes together, we show that the phonon blockade effect is enhanced compared to the regime without MPA. What is more, the two-time second-order correlation function gradually tends to one without rapid oscillations in our scheme, which suggests that high time resolution is not necessary in the detection.