Controlling multiple optomechanically induced transparency in the distant cavity-optomechanical system

We theoretically investigate a two-cavity optomechanical system in which each optical cavity couples to a mechanical resonator via radiation pressure force, and the two optical cavities couple to each other via a distant waveguide. Our study shows that the multiple optomechanically induced transparency can be observed from the output field at the probe frequency. The number and width of the transparent windows can be tuned by the classical driving power P_l. We also analyze the distance of the two outermost transparency windows, which shows a linear relation with the parameters P_l and Λ. Our approach is feasible for controlling multipartite induced transparency, which represents a valuable step towards quantum networks with photonic and phononic circuits.