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arXiv:0805.2110 · International Journal of Quantum Information

A CASE OF ENTANGLEMENT GENERATION BETWEEN CAUSALLY DISCONNECTED ATOMS

Juan León, Carlos Sabín

Published Jan 1, 2009• 4 citations
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Abstract

We analyze the entanglement generated in a finite time between a pair of space-like separated atoms, one of which emits a photon. As we show to order e2, the origin of entanglement can be traced back to the uncertainty about which one of the atoms emitted the photon. We check this by comparing the time behaviors of the emission processes allowed by energy conservation versus those forbidden by the same reason. No physical signal propagates between the atoms in the processes considered, however an effective light cone separating non-entangled from entangled regions in space-time emerges from our calculations.

DOI
10.1142/s0219749909004773

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We analyze the entanglement generated in a finite time between a pair of space-like separated atoms, one of which emits a photon. As we show to order e2, the origin of entanglement can be traced back to the uncertainty about which one of the atoms emitted the photon. We check this by comparing the time behaviors of the emission processes allowed by energy conservation versus those forbidden by the same reason. No physical signal propagates between the atoms in the processes considered, however an effective light cone separating non-entangled from entangled regions in space-time emerges from our calculations.
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.
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The Feynman propagator has nonzero values outside of the forward light cone. That does not allow messages to be transmitted faster than the speed of light, but it is shown here that it does allow entanglement and mutual information to be generated at space-like separated points. These effects can be interpreted as being due to the propagation of virtual photons outside of the light cone or as a transfer of pre-existing entanglement from the quantum vacuum. The differences between these two interpretations are discussed.
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We investigate, in the case of the $2P\text{\ensuremath{-}}1S$ transition in atomic hydrogen, the behavior of the spontaneously emitted electromagnetic field in space-time. We focus on Glauber's wave function for the emitted photon, a quantity which we find is nonzero outside the light cone at all times after the start of the emission. We identify the uncertainty on the position of the decaying electron as a source of departure from causality in the naive sense of the term. We carry out a detailed study of the emitted electric field in the mid- and far-field regions, through analytical and numerical computations as well as asymptotic arguments.
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.