▎ 摘　　要

We demonstrate theoretically the slow and fast light effects based on the coupled graphene nanomechanical resonator-microwave cavity system. The numerical results show that the maximum group delay and advancing microwave signals can reach 0.4 and 0.12 ms, respectively, in the graphene resonator-microwave cavity system. In addition, the system can also behave as an optical transistor to amplify a weak microwave field through manipulating the pump field. Further we investigate the nonlinear effects of four-wave mixing (FWM) and show that the FWM intensity can be efficiently controlled and modulated by the pump power. The graphene optomechanics provides a good medium for controlling microwave photons at different frequencies and may indicate applications in quantum information processing.