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arXiv:0807.2711 · Physical Review A

Entanglement swapping between spacelike-separated atoms

Juan León, Carlos Sabín

Published Nov 10, 2008• 11 citations
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Abstract

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.

DOI
10.1103/physreva.78.052314

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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 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.
We analyze whether a pair of neutral two level atoms can become entangled in a finite time while they remain causally disconnected. The interaction with the electromagnetic field is treated perturbatively in the electric dipole approximation. We start from an initial vacuum state and obtain the final atomic correlations for the cases where n=0n=0n=0, 1, or 2 photons are produced in a time ttt, and also when the final field state is unknown. Our results show that correlations are sizable inside and outside the mutual light cone for n=1n=1n=1 and 2, and also that quantum correlations become classical by tracing over the field state. For n=0n=0n=0 we obtain entanglement generation by photon propagation between the atoms, the correlations come from the indistinguishability of the source for n=1n=1n=1, and may give rise to entanglement swapping for n=2n=2n=2.
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 report the experimental realization of entanglement swapping over long distances in optical fibers. Two photons separated by more than 2km2\phantom{\rule{0.3em}{0ex}}\mathrm{km}2km of optical fibers are entangled, although they never directly interacted. We use two pairs of time-bin entangled qubits created in spatially separated sources and carried by photons at telecommunication wavelengths. A partial Bell-state measurement is performed with one photon from each pair, which projects the two remaining photons, formerly independent onto an entangled state. A visibility high enough to infer a violation of a Bell inequality is reported, after both photons have each traveled through 1.1km1.1\phantom{\rule{0.3em}{0ex}}\mathrm{km}1.1km of optical fiber.