Generation of atom-atom correlations inside and outside the mutual light cone

TL;DR

This paper investigates the generation and nature of atom-atom correlations, including entanglement, inside and outside the light cone, considering different photon production scenarios and their implications for quantum information transfer.

Contribution

It provides a detailed analysis of how atomic correlations and entanglement can arise in relativistic settings with varying photon numbers, including cases of classical and quantum correlations.

Findings

Correlations are significant both inside and outside the light cone for n=1 and 2.

Quantum correlations can become classical when the field state is traced out.

Entanglement can be generated through photon propagation and indistinguishability effects.

Abstract

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 e. m. 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 = 0, 1, or 2 photons are produced in a time t, 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= 1 and 2, and also that quantum correlations become classical by tracing over the field state. For n = 0 we obtain entanglement generation by photon propagation between the atoms, the correlations come from the indistinguishability of the source for n = 1, and may give rise to entanglement swapping for n = 2.