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arXiv:0911.3564 · Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of entanglement between two free atoms with quantized motion

F. Lastra, Sascha Wallentowitz

Published Jun 1, 2010• 3 citations
arXivHTMLPDF

Abstract

The electronic entanglement between two free atoms initially at rest is obtained including the effects of photon recoil, for the case when quantum dispersion can be neglected during the atomic excited-state lifetime. Unlike previous treatments using common or statistically independent reservoirs, a continuous transition between these limits is observed, which depends on the inter-atomic distance and degree of localization. The occurrence of entanglement sudden death and birth as predicted here deviates from the case where the inter-atomic distance is treated classically by a static value. Moreover, the creation of a dark state is predicted, which manifests itself by a stationary entanglement that even may be created from an initially separable state.

DOI
10.1088/0953-4075/43/12/125501

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The electronic entanglement between two free atoms initially at rest is obtained including the effects of photon recoil, for the case when quantum dispersion can be neglected during the atomic excited-state lifetime. Unlike previous treatments using common or statistically independent reservoirs, a continuous transition between these limits is observed, which depends on the inter-atomic distance and degree of localization. The occurrence of entanglement sudden death and birth as predicted here deviates from the case where the inter-atomic distance is treated classically by a static value. Moreover, the creation of a dark state is predicted, which manifests itself by a stationary entanglement that even may be created from an initially separable state.
We consider two two-level atoms, which are located in two independent dissipative cavities. The two atoms are initially prepared in the singlet state. We investigate the influence of dissipation on the entanglement between the two atoms. In the case of resonance the degree of the entanglement can fall abruptly to zero, which is the so-called sudden death of entanglement. It is noted that when two atoms are in a common environment, the singlet state is a decoherence-free state. When the dispersive limit is fulfilled, the degree of entanglement between the two atoms is oscillating at first, then it arrives at a steady value, which increases with the increase of the damping constant κ; when both fields are initially in the vacuum state, the entanglement between the two atoms will not decay.
An investigation is reported of the collective effects and the dynamics of atom–atom entanglement in a system of two distant two-level atoms which are coupled via an optical element. In the system under consideration, the two atoms, which are trapped in the foci of a lens, are coupled to a common environment being in the vacuum state and they emit photons spontaneously. A fraction of the emitted photons from each atom is thus focused on the position of the other atom. The presence of optical element between two distant atoms leads to the occurrence of delayed collective effects, such as delayed dipole–dipole interaction and delayed collective spontaneous emission, which play the crucial role in the dynamical behaviour of the entanglement. We discuss the phenomena of entanglement sudden birth, entanglement sudden death, and revival of entanglement for both cases of initial one-photon and initial two-photon unentangled atomic states. We show that the evolution of the entanglement is sensitive not only to the interatomic distance but also to the initial state of the system as well as to the properties of the optical element.
We discuss a simple model for creation of entanglement in a system composed of two two-level atoms interacting with a common environment. The role of the environment in entangling and disentangling of the atoms is explored. We demonstrate how the spontaneous decay of an initial excitation of the system can create a transient entanglement between the atoms. The opposite situation is also discussed where a spontaneous disentanglement of initially entangled atoms may exhibit some unusual features such as entanglement sudden birth, the phenomenon of entanglement sudden death and revival of entanglement. We provide a discussion of these unusual phenomena in terms of the density matrix elements of the system and show the connection of the phenomena with the threshold behaviour of the concurrence.
Entanglement is a fundamental concept in quantum mechanics. In this review, we study various aspects of coherence and entanglement, illustrated by several examples. We relate the concepts of loss of coherence and disentanglement, via a model of two two-level atoms in different types of reservoir, including cases of both independent and common baths. Finally, we relate decoherence and disentanglement, by focusing on the sudden death of the entanglement and the dependence of the death time with the distance of our initial condition from the decoherence-free subspace. In particular, we study the sudden death of the entanglement in a two-atom system with a common reservoir.
We consider the time evolution of quantum entanglement in the context of interactions between atoms and the electromagnetic field. We explore the influence of interatomic separation and the degree to which this can change the qualitative character of those dynamics, including entanglement generation, protection, and sudden death (SD). We find that the qualitative features of entanglement dynamics can be changed entirely in few-mode models when atomic spacing is varied, allowing for particular choices of configuration that are favorable for maintaining entanglement. We also examine the inaccuracies introduced by the use of common approximations: We characterize unexpected errors that result from using perturbative master equations as well as those that result from using the rotating-wave approximation (RWA). We find that in dissipative systems the errors introduced by these approximations can lead to an incorrect picture of late-time dynamics. Standard perturbative master equations using the RWA are constrained to predict that late-time SD occurs to only some initial states at zero temperature, but this is merely an artifact of those approximation and generally not correct. The same master equations predict that at finite temperature all states are separable asymptotically at late times and must undergo SD. In fact a proper accounting of environmentally-induced corrections to the steady state of the system shows that for low temperatures it is possible to have asymptotic entanglement in some cases. We derive a master equation for two atoms interacting with the free field without using the RWA and solve it to obtain the dynamics, including the effects of distance. From these dynamics we find that, in fact, all initial states of atoms separated by any positive distance undergo SD even at zero temperature, though there are sub-radiant states that can be quite long-lived for closely spaced atoms.