  Entanglement properties of two uncoupled atoms embedded in a coherent field
distribution through one quantum transition process is studied. A case of
non-linear Hamiltonian of the problem is considered through which the effect of
a non-linear media is illustrated. Moreover, the effect of the frequency
difference between the interatomic transition and the electromagnetic field is
also analyzed. We show that, adjusting the considered parametres of the
non-linear media and frequency difference leads to a strong control of the
degree of entanglement where excellent periodicity of entanglement evolution
can be obtained which is very important in predicting the behavior of
transmitted information through the application of various information
processing schemes. We present a detailed and comparative study of atom-atom
entanglement for two cases corresponding to different injections of the two
atoms into the cavity field. Moreover, we present an answer to the question:
How does the quantum phase space structure for a composite system relate to the
entanglement characteristics of the corresponding quantum system? We
demonstrate how the entanglement in nonlinear tripartite systems can be
associated with a delocalization in the phase space distribution.
