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

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.

Local modulation of double optomechanically induced transparency and amplification.

We consider the probe absorption properties in a mechanically coupled optomechanical system in which the two coupled nanomechanical oscillators are driven by the time-dependent forces, respectively. It is found that the mechanical interaction splits the transparency window for a usual single-mode optomechanical system into two parts and then leads to appearance of the double optomechanically induced transparency. The distance between the two transparency positions (the frequency for the maximal transparency) is determined by the mechanical interaction amplitude. This can be explained by using optomechanical dressed-mode picture which is analogue to the interacting dark resonances in coherent atoms. When the mechanical resonators are driven by the external forces, the transparencies in the double-transparency spectrum can be increased into amplifications or be suppressed by tuning the amplitude of the forces. Additionally, it is shown that the double transparencies or the amplifications oscillate with the initial phases of the forces with a period of 2π. These investigations will be useful for more flexible controllability of multi-channel optical communication based on the optomechanical systems.