Cross-Kerr effect in a parity-time symmetric optomechanical system.

Abstract

The cross-Kerr effects between the cavity and the mechanical oscillator in a parity-time symmetric optomechanical system are investigated. It is found that in the double-passive case there appears an asymmetric optomechanically induced transparency (OMIT) spectrum which is composed of a broad absorption peak located around the resonant point and a absorption line at the frequency position mainly determined by the Kerr interaction. The distinctive asymmetry induced by the cross-Kerr coupling is precisely demonstrated by the analytic findings. In the passive-active case, the resonance peaks in the OMIT spectrum are increased with the weak tunnel coupling, which is contrary to that in the double-passive case. When the tunnel coupling is increased up in the strong coupling region, the broad absorption peak and the absorption line in the OMIT spectrum are sequentially changed into the amplification ones, and the central amplification dip is split into two parts due to the normal mode splitting induced by the strong tunnel coupling. This can be used to realize a switching from absorption to amplification by only adjusting the tunnel interaction.