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Entanglement properties of two uncoupled atoms embedded in a coherent fielddistribution through one quantum transition process is studied. A case ofnon-linear Hamiltonian of the problem is considered through which the effect ofa non-linear media is illustrated. Moreover, the effect of the frequencydifference between the interatomic transition and the electromagnetic field isalso analyzed. We show that, adjusting the considered parametres of thenon-linear media and frequency difference leads to a strong control of thedegree of entanglement where excellent periodicity of entanglement evolutioncan be obtained which is very important in predicting the behavior oftransmitted information through the application of various informationprocessing schemes. We present a detailed and comparative study of atom-atomentanglement for two cases corresponding to different injections of the twoatoms 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 theentanglement characteristics of the corresponding quantum system? Wedemonstrate how the entanglement in nonlinear tripartite systems can beassociated with a delocalization in the phase space distribution.

An investigation of a nonlocal entanglement of two uncoupled atoms  embedded in a coherent cavity field and the associated phase space  distribution: one quantum non-linear process