  This communication 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 role in the evolution of
the sub-entropies and entanglement.
