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

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 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 $n=0$, 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 $n=2$.