Phonon blockade and strong anti-correlation between phonons and phonons in the optomechanical system with an auxiliary mechanical oscillator

Abstract

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.