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This paper is an enquiry into the circumstances under which entropy and subentropy methods can give an answer to the question of quantum entanglement in the composite state. Using a general quantum dynamical system, we obtain the analytical solution when the atom initially starts from its excited state and the field in different initial states. Different features of the entanglement are investigated when the field is initially assumed to be in a coherent state, an even coherent state (Schrodinger cate state), and a statistical mixture of coherent states. Our results show that the setting of the initial state and the Stark shift play important roles in the evolution of the sub-entropies and entanglement.

A TREATMENT OF THE QUANTUM PARTIAL ENTROPIES IN THE ATOM-FIELD INTERACTION WITH A CLASS OF SCHRÖDINGER CAT STATES