In this paper, we study the time evolution of the entropies and the degree of entanglement
in the mixed state for a multi-quanta JC model taking into consideration Stark shift and
Kerr-like medium effect, we use a numerical method to investigate the time evolution
of the partial entropy of the atom and field subsystem. This is done in the framework of
themulti-quanta presses JCmodel with both the Stark shift and Kerr-likemedium effect
added. Furthermore, we examine the effect of the superposition states and a statistical
mixture of coherent states as an initial field on the entropies and entanglement. Our
results show that the setting of the initial state play an important role in the evolution
of the sub-entropies and entanglement.