Control of electromagnetically induced transparency and Fano resonances in a hybrid optomechanical system

We study the control of electromagnetically induced transparency and Fano resonances in a hybrid optomechanical system based on Bose-Einstein condensate trapped inside a high finesse Fabry Perot cavity coupled with two charged nanomechanical resonators. The system is driven by a pump field and probed by a probe field. The nanomechanical resonators are connected to an external bias voltage V-1(-V-2) and generated electrostatic Coulomb coupling g(c). In this study, we show that the electromagnetically induced transparency can be controlled by the s-wave scattering frequency omega(sw) as well as by the coupling frequencies of the system. Further, studying the effect of Bogoliubov mode, the transparency window splits from double to triple windows. At strong atom-atom interaction, we explain the asymmetric windows' and explain their physical understanding.