An efficiently and tunable switch between slow- and fast-light in double mode with an optomechanical system

We study the dynamics of a driven optomechanical cavity coupled to a charged nanomechanical resonator via Coulomb interaction. We find the tunable switch between slow-and fast- light in double-mode can be observed from the output field by adjusting the laser-cavity detuning in this coupled system. Moreover, the requencies of signal light can be tuned by Coulomb coupling strength. The proposal may have potential application in optical communcation and nonlinear optics.