Controllable and tunable multiple optomechanically induced transparency and Fano resonance mediated by different mechanical resonators

We demonstrate the multiple optomechanically induced transparency (OMIT) and Fano resonance in a hybrid optomechanical system, in which an optical cavity is coupled to two mechanical resonators with interaction (such as Coulomb interaction) via radiation pressure. The probe transmission spectra experience the transition from single-mode OMIT to multiple OMIT with controlling the interaction of the two resonators, and we discuss the robustness of the system against the cavity decay rate. Compared with the situation of without considering the interaction of the two resonators, the transmission spectra present asymmetric Fano line shapes via manipulating the optomechanical coupling strengths between the optical cavity and the two resonators with taking into account the resonator interaction. Furthermore, we compare the results of identical mechanical resonators with the same mass and frequencies to different mechanical resonators with different mass and frequencies. The results indicate that the probe transmission spectra undergo a series of transition from Fano resonances to OMIT by controlling the different mechanical resonators as well as the interaction between the two mechanical resonators, and we can present a scheme to determine the resonator interaction via measuring the peaks splitting. Finally, the transparency windows in the probe transmission spectrum are accompanied by the rapid normal phase dispersion under different mechanical resonators, which may indicate the slow and fast light effect.