We analyze some aspects of the internal and translational dynamics of a two-level atom interacting with a resonant standing wave of an ideal cavity. We show that the cavity vacuum field can split the incoming wave packet of the excited two-level atom into two parts, whose scalar product in the Hilbert space determines the behavior of the Rabi oscillations. The state of the whole system is derived and allows us to study the correlations between the internal and the translational atomic dynamics. We find that these correlations become negligible when the two parts are sufficiently away from each other in the space.

Rabi oscillations may be viewed as an interference phenomenon due to a coherent superposition of different quantum paths, like in the Young's two-slit experiment. The inclusion of the atomic external variables causes a non dissipative damping of the Rabi oscillations. More generally, the atomic translational dynamics induces damping in the correlation functions which describe non classical behaviors of the field and internal atomic variables, leading to the separability of these two subsystems. We discuss on the possibility of interpreting this intrinsic decoherence as a "which-way" information effect and we apply to this case a quantitative analysis of the complementarity relation as introduced by Englert [Phys. Rev. Lett. 77, 2154]. Young's double-slit experiment may be considered as an emblematic example to introduce the wave-particle duality, which, to quote Feynman [1], is the basic mystery of Quantum Mechanics (QM). This experiment is frequently discussed in the introductory part of QM textbooks [2] to explain how the interference pattern and the which-way information on the particle trajectory are mutually exclusive behaviors in QM. Moreover, this wave-particle dualism belongs to the enlarged contest of complementarity [3,4], which has its root in the superposition principle. Coherent superposition of two states or, more generally, of two quantum paths leads to interference effects which may manifest itself as probability oscillations of some "populations". For example, when a two-level atom interacts with the field of an optical cavity, the atomic level populations undergo to the well known Rabi oscillations. But, what is the interference effect underlying this phenomenon? In other words, which paths do interfere? When the atomic external degrees of freedom are included in the model, the internal dynamics of the atom correlates with the translational variables. This information transfer towards the atomic external variables is at the origin of an intrinsic decoherence effect, that is, it causes a non dissipative damping of the Rabi oscillations [5,6]. Non dissipative damping of Rabi oscillations has been observed experimentally [7,8] and it has also been analyzed by Bonifacio et. al. who consider the evolution time as random variable [9]. In this letter we will show that a damping also affects all the correlations functions which are involved in the Bell inequality [10] and in the separability criterion [11,12] for the field and atomic internal variables. Can this decoherence be interpreted as a "which-way" information effect? In this Letter we will try to throw light on these questions. Let us consider a two-level atom interacting with the field of an optical cavity. In the rotating wave approximation (RWA) the atom-field interaction is described by the Hamiltonian ǫ sin kx(â †Ŝ − +âŜ + ) , where the usual spin 1/2 operators refer to the internal dynamics of the two-level atom, whileâ andâ † are the annihilation and creation operators for the photons of k-mode of the cavity standing wave and ǫ is the at...

Recently, it has been realized that nonlocal disentanglement may take a finite time as opposite to the asymptotic decay of local coherences. We find in this paper that a sudden irreversible death of entanglement takes place in a two atom optical Stern-Gerlach model. In particular, the one degree non dissipative environment here considered suddenly destroys the initial entanglement of any Bell's states˛φ ±¸s uperposition.

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. 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.PACS numbers: 32.80.Lg, 03.65.Ud A necessary condition for attaining fruitful teleportation [1] is the possibility of constructing "non locally" correlated systems. Recently, it has been payed attention to teleportation of massive particles and, more generally, to non-local correlations, separability and related issues [2,3,4,5,6,7,8]. A simple model which can realize an EPR state consists of two atoms which interact successively with the field of an optical cavity. As a consequence of the entanglement developed during the interaction between the first atom and the field, quantum correlations between the two atoms do arise as the second one interacts with the field of the same cavity. Using the standard Jaynes-Cummings (JC) model, non-local correlations have been predicted [4] which can lead to a violation of the Bell's inequality. In this letter we suggest that a careful analysis of the interatomic correlations may require the quantization of the translational dynamics of the two atoms along the cavity axis. In fact, it is here shown that the quantization of the translational dynamics affects the non-local features of the interatomic correlations, at least when the atoms enter the cavity in a region where the field gradient is different from zero (for example in a nodal region). To take into account these translational effects, we adopt the optical Stern-Gerlach (SG) model [9] for the atom-field interaction, while to investigate on the non-local features we test the Bell's inequality [10] and the separability [11,12] for the reduced density matrix describing the internal degrees of freedom of the two atoms, after their interaction with the cavity. For this system our main quantitative result reveals the appearance of damping terms in the correlation functions of the two-atom internal variables, induced by the entanglement with the translational dynamics. These damping factors destroy the quantum nature of the correlations just for an interaction time of a few Rabi oscillations. Let us consider a system composed by two two-level atoms interacting, not simultaneously, with the e.m. field of the same undamped cavity. At the time t = 0, the first atom, say A 1 , enters the cavity moving prevalently along the z-direction, orthogonal to the x-cavity axis, and interacts with the field for a time t 1 . We assume that the atomic velocity along t...