Phase-dependent double optomechanically induced transparency in a hybrid optomechanical cavity system with coherently mechanical driving

We propose a scheme that can generate tunable double optomechanically induced transparency in a hybrid optomechanical cavity system. In this system, the mechanical resonator of the optomechanical cavity is coupled with an additional mechanical resonator and the additional mechanical resonator can be driven by a weak external coherently mechanical driving field. We show that both the intensity and the phase of the external mechanical driving field can control the propagation of the probe field, including changing the transmission spectrum from double windows to a single-window. Our study also provides an effective way to generate intensity-controllable, narrow-bandwidth transmission spectra, with the probe field modulated from excessive opacity to remarkable amplification.