Information entropy of multi-photon field interacting with single-qubit circuit

We study the interaction of the single-Cooper pairbox interacting with a cavity field. The solution of the system dynamics is obtained. The entropy as a measure of the entanglement between the qubit and the field is calculated and compared with the field purity. It is shown that the general behavior of the entropy as well as the field purity is affected in the same way under different values of the system parameters.