Dynamic behaviour of a single-Cooper-pair box in a single-mode quantized field with dissipation

We study the quantum dynamics of a single-Cooper-pair box biased by a classical voltage and also irradiated by a single-mode quantized field. We demonstrate that under the weak damping, the collapse-revival phenomena can exist in this system. We also demonstrate that the revivals of oscillations are sensitive to the initial coherent field and the damping rate of the single-mode quantized field.