Here we propose a scheme to realize phonon blockade in a cascaded coupling optomechanical system, where a quadratically coupled optomechanical system couples with a mechanical oscillator. The strong nonlinear interaction between photons and phonons in the quadratically coupled optomechanical system is induced by an external field. Meanwhile the linear coupling between the mechanical resonator and the oscillator provides interference paths. Based on the destructive quantum interference, the two mechanical oscillators both can exhibit phonon blockade even that the nonlinearities in the optomechanical system are weak. The optimal condition of phonon blockade is analytically calculated and coincides with the numerical simulation. In the condition of weak driving on cavity, the two oscillators can exhibit phonon blockade in the same parameter regime. In addition, the strong anti-correlation between phonons and phonons can be observed and the correlated phonon pairs is generated in the weak nonlinear coupling condition. Utilizing the cascaded coupling optomechanical system, our scheme provides a possible way to experimentally generate the anti-correlated phonons as well as a two-phonon gateway.

在这里，我们提出了一种在级联耦合光机系统中实现声子阻塞的方案，其中二次耦合光机系统与机械振荡器耦合。二次耦合光机械系统中光子和声子之间的强非线性相互作用是由外场引起的。同时，机械谐振器和振荡器之间的线性耦合提供了干扰路径。基于破坏性量子干涉，即使光机械系统中的非线性很弱，两个机械振荡器都可以表现出声子阻塞。对声子阻滞的最佳条件进行了解析计算，与数值模拟吻合。在腔体弱驱动条件下，两个振荡器可以在相同的参数范围内表现出声子阻塞。此外，可以观察到声子和声子之间的强反相关，并且相关声子对是在弱非线性耦合条件下产生的。利用级联耦合光机系统，我们的方案提供了一种可能的方法来实验生成反相关声子以及双声子网关。