Microwave field controlled slow and fast light with a coupled system consisting of a nanomechanical resonator and a Cooper-pair box

We theoretically demonstrate an efficient method to control slow and fast light in microwave regime with a coupled system consisting of a nanomechanical resonator (NR) and a superconducting Cooper-pair box (CPB). Using the pump-probe technique, we find that both slow and fast light effects of the probe field can appear in this coupled system. Furthermore, we show that a tunable switch from slow light to fast light can be achieved by only adjusting the pump-CPB detuning from the NR frequency to zero. Our coupled system may have potential applications, for example, in optical communication, microwave photonics, and nonlinear optics.