Abstract
We study the photon statistics of a cavity linearly coupled to an optomechanical system via second order correlation functions. Our calculations show that the cavity can exhibit strong photon antibunching even when optomechanical interaction in the optomechanical system is weak. The cooperation between the weak optomechanical interaction and the destructive interference between different paths for two-photon excitation leads to the efficient antibunching effect. Compared with the standard optomechanical system, the coupling between a cavity and an optomechanical system provides a method to relax the constraints to obtain single photon by optomechanical interaction.
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