A case of entanglement generation between causally disconnected atoms

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 $e^2$, 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 vs. 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.