Coulomb-enhanced transparency and prolonged slow light in a linear and quadratic optomechanical system

We explore novel optomechanically induced transparency (OMIT) and prolonged slow light in a linear and quadratic optomechanical system (OMS) with the Coulomb coupling. The hybrid OMS includes a Fabry–Pérot cavity and two charged mechanical resonators (MR1 inside the cavity and MR2 outside the cavity), where the interaction between the charged MR1 and the cavity field are both linear and quadratic in the MR1’s displacement, and the charged MR1 and the charged MR2 mutually coupled via Coulomb interaction. Specifically, the transmission of the output field exhibits three transparency window dips. The Coulomb coupling strength is responsible for creating two transparency window dips near \(\delta /{\omega _m} = 1\) $\delta /{\omega }_m=1$ , which results from the mechanical dressed mode. Simultaneously, the quadratic coupling between the charged MR1 and the optical cavity field significantly contributes to another transparency window dip near \(\delta /{\omega _m} = 2\) $\delta /{\omega }_m=2$ , which is attributed to the two-phonon process. In addition, by adjusting the value of Coulomb coupling strength, linear (quadratic) coupling and frequency of the two mechanical resonators, one can attain prolonged slow light with a group delay extending to tens of milliseconds. Furthermore, the positive (negative) value of quadratic coupling strength can determine the switching behavior of the group delay (i.e., from superluminal to subluminal propagation) on the right (left) side of \(\delta /{\omega _m} =2\) $\delta /{\omega }_m=2$ . We believe that the results have potential applications in manipulating the performance of OMIT devices and optical switching.