Detectors interacting through quantum fields: Non-Markovian effects, non-perturbative generation of correlations and apparent non-causality

TL;DR

This paper provides an exact analysis of two detectors interacting via a quantum field, revealing non-Markovian effects, non-perturbative correlation generation, and apparent non-causality, challenging common approximations in quantum field measurements.

Contribution

It offers an exact solution to a two-detector system, highlighting limitations of standard approximations and exploring causality and entanglement in relativistic quantum systems.

Findings

Common approximations fail at large distances.

Asymptotic state is correlated but not entangled unless separated by a wavelength.

Local observables exhibit non-causal evolution.

Abstract

We study the system of two localized detectors (oscillators) interacting through a massless quantum field in a vacuum state via an Unruh-DeWitt coupling. This system admits an exact solution providing a good model for addressing fundamental issues in particle-field interactions, causality and locality in quantum field measurements that are relevant to proposed quantum experiments in space. Our analysis of the exact solution leads to the following results. (i) Common approximations used in the study of analogous open quantum systems fail when the distance between the detectors becomes of the order of the relaxation time. In particular, the creation of correlations between remote detectors is not well described by ordinary perturbation theory and the Markov approximation. (ii) There is a unique asymptotic state that is correlated; it is not entangled unless the detector separation is of the order of magnitude of the wavelength of the exchanged quanta. (iii) The evolution of seemingly localized observables is non-causal. The latter is a manifestation of Fermi's two-atom problem, albeit in an exactly solvable system. We argue that the problem of causality requires a reexamination of the notion of entanglement in relativistic systems, in particular, the physical relevance of its extraction from the quantum vacuum.