Properties of the output field of a hybrid superconducting quantum circuit system

We consider the optical-response properties in a hybrid superconducting circuit system, composed of a superconducting transmission-line microwave cavity, a nanomechanical oscillator and a superconducting qubit. We find that the addition of the qubit in the system can decrease the effective detuning and the effective decay of the cavity. By adjusting the field–qubit coupling, our system can achieve a tunable transparency window, and more importantly, it can realize the amplification of the weak probe field. Furthermore, we also find that our system can achieve slow-light propagation, and the group delay of the probe field can be increased significantly by increasing the field–qubit coupling. (paper)