Translational dynamics effects on the non-local correlations between two atoms

A pair of atoms interacting successively with the field of the same cavity and exchanging a single photon, leave the cavity in an entangled state of Einstein-Podolsky-Rosen (EPR) type (see, for example, [S.J.D. Phoenix, and S.M. Barnett, J. Mod. Opt. \textbf{40} (1993) 979]). By implementing the model with the translational degrees of freedom, we show in this letter that the entanglement with the translational atomic variables can lead, under appropriate conditions, towards the separability of the internal variables of the two atoms. This implies that the translational dynamics can lead, in some cases, to difficulties in observing the Bell's inequality violation for massive particles.