Controlling double optomechanically induced transparency and slow/fast light in an electro-optomechanical system via an optical parametric amplifier

We investigate tunable double optomechanically induced transparency and slow/fast phenomena in a hybrid electro-optomechanical system. The hybrid system consists of an optical cavity with an optical parametric amplifier (OPA) and two charged mechanical resonators. The double optomechanical induce transparency can be exhibited by manipulating the coupling parameters of the electro-optomechanical system. Specifically, the number of transparent points and the width of transparent windows increase with an increase in the coupling constant. Furthermore, the phenomenon of double transparency is strongly influenced by the parametric gain of OPA and by the Coulomb interaction between the two mechanical oscillators. It is found that the larger parametric gain and Coulomb coupling induce an increasing width of transparency windows. Moreover, we study the slow/fast light effect associated with the rapid phase change of the transmission of probe field. Our approach provides a great flexibility for controlling double induced transparency, and has potential applications in optical information storage and optical communication.