Abstract
A system of a Cooper pair box interacting with a field in the binomial state is considered in the dispersive regime. The system is coupled to the environment through phase damping. The effects of the different parameters on the purity of the states of the total system and the subsystems are considered. It is found that damping does not affect the state of the box. While it affects the state of the field and the total system. The initial state of the box has the dominant effect on the heights of oscillations on both the field and the box states.