Mutual entropy of a single Cooper pair-box interacting with multi-photon field

We discuss the interaction of a single Cooper pair box interacting with a multi-photon field. The dynamical behavior is investigated using the quantum mutual entropy. The results show that the system parameters (the number of quanta and detuning parameters) play an important role in entanglement. This result might shed the light on the possibility to use the number of quanta as a controller parameter for the present system.