Multiple electromechanically-induced-transparency windows and Fano resonances in hybrid nano-electro-optomechanics

We show multiple electromechanically-induced transparency (EMIT) windows in a hybrid nano-electro-optomechanical system in the presence of two-level atoms coupled to a single-mode cavity field. The multiple EMIT-window profile can be observed by controlling the atom field coupling as well as Coulomb coupling between the two charged mechanical resonators. We derive the analytical expression of the multiple-EMIT-windows profile and describe the splitting of multiple EMIT windows as a function of optomechanical coupling, atom-field coupling, and Coulomb coupling. In particular, we discuss the robustness of the system against the cavity decay rate. We compare the results of identical mechanical resonators to different mechanical resonators. We further show how the hybrid nano-electro-optomechanics coupled system can lead to the splitting of the multiple Fano resonances (MFR). The Fano resonances are very sensitive to decay terms in such systems, i.e., atoms, cavities, and the mechanical resonators.