Optomechanically induced transparency in a hybrid system containing two-level atomic ensemble and optical parametric amplifier

We investigate the physical properties of multiple optomechanically induced transparency in a system. The system consists of two charged mechanical resonators and an optical cavity. An optical parametric amplifier (OPA) and a two-level atom ensemble are filled into the optical cavity. Some physical phenomena appear in the system driven by the probe field and the pump field. The width of transparent windows can be manipulated by the coupling strengths of the system. Specifically, the width of the transparency window increases with an increase in the parametric gain of the optical parametric amplifier (OPA). Furthermore, the number of transparent windows and the location of transparent points are also affected by the system parameters. The presence of two-level atomic ensemble causes the double transparent windows to be split three transparent windows. The Coulomb coupling between the two charged mechanical resonators causes the transparent points to move. Our approach provides a great flexibility for manipulating multiple induced transparency. It is helpful to study the quantum properties of nonlinear optical systems.