Localized projective measurement of a quantum field in non-inertial frames

Abstract

We propose a projective operator formalism that is well-suited to study the correlations of quantum fields in non-inertial frames and curved spacetimes. We generalize a Glauber model of detection of a single localized field mode to allow for making measurements in an arbitrary reference frame. We show that the model correctly reproduces the Unruh temperature formula of a single accelerated detector, and use it to extract vacuum entanglement by a pair of counter-accelerating detectors. This latter example is a proof of principle that this approach will be appropriate to further studies on the nature of entanglement in curved spacetimes and, in general, to model experimentally feasible scenarios in quantum field theory in non-inertial frames. Finally, as further confirmation of the validity of our approach, we introduce an explicit perturbative matter–radiation interaction model and show that under uniform acceleration it reproduces both the generalized Glauber model and the projective measurement results in the weak coupling regime.