Abstract
We theoretically investigate the optomechanically induced transparency (OMIT) phenomenon in a N-cavity optomechanical system doped with a pair of Rydberg atoms with the presence of a strong control field and a weak probe field applied to the Nth cavity. It is found that 2N - 1 (N < 10) numbers of OMIT windows can be observed in the output field when N cavities couple with N mechanical oscillators and the mechanical oscillators coupled with different even- or odd-labelled cavities can lead to diverse effects on OMIT. Furthermore, the ATS effect appears with the increase of the effective optomechanical coupling rate. On the other hand, two additional transparent windows (extra resonances) occur, when two Rydberg atoms are coupled with the cavity field. With DDI strength increasing, the extra resonances move to the far off-resonant regime but the left one moves slowly than the right one due to the positive detuning effect of DDI. During this process, Fano resonance also emerges in the absorption profile of output field.