Violating Bell’s inequalities in vacuum

Abstract

We employ an approach wherein the ground state entanglement of a relativistic free scalar field is directly probed in a controlled manner. The approach consists of having a pair of initially nonentangled detectors locally interact with the vacuum for a finite duration $T$, such that the two detectors remain causally disconnected, and then analyzing the resulting detector mixed state. We show that the correlations between arbitrarily far-apart regions of the vacuum cannot be reproduced by a local hidden-variable model, and that as a function of the distance $L$ between the regions, the entanglement decreases at a slower rate than $\ensuremath{\sim}\mathrm{exp}[\ensuremath{-}{(L∕cT)}^{3}]$.