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arXiv:0810.2246

Atom-atom entanglement generated at early times by two photon emission

Juan León, Carlos Sabín

Published Oct 13, 2008• 0 citations
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Abstract

We analyze entanglement generation between a pair of neutral two level atoms that are initially excited in a common electromagnetic vacuum. The nonlocal correlations that appear due to the interaction with the field can become entanglement when the field state is known. We distinguish two different situations: in the first, the field remains in the vacuum state, and second two photons are present in the final state. In both cases we study the dependence of the entanglement with time and interatomic distance, at ranges related with locality issues.

DOI
10.48550/arxiv.0810.2246

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We show a mechanism that projects a pair of neutral two-level atoms from an initially uncorrelated state to a maximally entangled state while they remain spacelike separated. The atoms begin both excited in a common electromagnetic vacuum, and the radiation is collected with a partial Bell-state analyzer. If the interaction time is short enough and a certain two-photon Bell state is detected after the interaction, a high degree of entanglement, even maximal, can be generated while one atom is outside the light cone of the other, for arbitrary large interatomic distances.
We analyze the entanglement dynamics of a system composed by a pair of neutral two-level atoms that are initially entangled, and the electromagnetic field, initially in the vacuum state, within the formalism of perturbative quantum field theory up to the second order. We show that entanglement sudden death and revival can occur while the atoms remain spacelike separated and therefore cannot be related with photon exchange between the atoms. We interpret these phenomena as the consequence of a transfer of atom-atom entanglement to atom-field entanglement and vice versa. We also consider the different bipartitions of the system, finding similar relationships between their entanglement evolutions.
We analyze the time evolution of quantum entanglement in a model consisting of two two-level atoms interacting with a two-mode electromagnetic field for a variety of initial states and interatomic separations. We study two specific atomic separations which give rise to symmetric atom-field couplings. For general atomic distances we consider a subset of initial states analytically, and then treat the more general situation numerically. We examine a variety of qualitative features such as entanglement sudden death, dynamical generation, protection, and transfer between subsystems. Our analysis shows a stark contrast in features of entanglement between the two special coupling schemes often considered; further, these features are uncharacteristic of those arising for general distances, due to the high degree of symmetry present in the special cases. The variety of behaviors in these two-mode cases suggest the importance of considering atomic separation carefully for any model where two atoms interact with a common field.
We study how the entanglement between two atoms can be created or modified even when they do not interact but when each of them interacts dispersively, i.e., weak and far from the resonance, with a single mode of the field. In particular, we study two cases: First we consider each atom to be initially in a pure state and secondly we assume that they start in a Werner state. Analytically we find that both atoms can, periodically, reach maximum entanglement if each of them starts in any state belonging to the Bloch sphere equator, independent of the initial Fock state of the mode. Thus, in particular, we find that a dispersive vacuum mode can generate entanglement between two two-level atoms. In the second case, when the field mode is initially in a coherent or thermal state we find that, in the high energy limit, in general there is no entanglement between the two atoms. However, at well defined moments, the initial entanglement appears and disappears suddenly, becoming a narrow entanglement-beats structure.
We analyze the time evolution of quantum entanglement in a model consisting of two two-level atoms interacting with a two-mode electromagnetic field for a variety of initial states. We study two different coupling schemes motivated by the forms that can arise due to atomic separation. We observe a variety of qualitative features such as entanglement sudden death, dynamical generation, protection, and transfer between subsystems. Our quantitative analysis shows that these cases with different couplings and initial states differ significantly in these qualitative features. The multifarious behaviors in these two-mode cases suggest the importance of considering atomic separation carefully for any model where two atoms interact with a common field.