Detectors for probing relativistic quantum physics beyond perturbation theory

TL;DR

This paper introduces a non-perturbative, formalism for harmonic-oscillator detectors in relativistic quantum fields, enabling exact analysis of phenomena like the Unruh effect, entanglement harvesting, and causal behavior across various setups.

Contribution

It develops a general, non-perturbative framework using continuous-variables techniques for harmonic detectors in relativistic quantum field theory, applicable to diverse physical scenarios.

Findings

Proves the Unruh effect non-perturbatively without Bogoliubov transformations.

Shows the emergence of causal behavior with multiple field modes.

Analyzes entanglement harvesting from the quantum vacuum.

Abstract

We develop a general formalism for a non-perturbative treatment of harmonic-oscillator particle detectors in relativistic quantum field theory using continuous-variables techniques. By means of this we forgo perturbation theory altogether and reduce the complete dynamics to a readily solvable set of first-order, linear differential equations. The formalism applies unchanged to a wide variety of physical setups, including arbitrary detector trajectories, any number of detectors, arbitrary time-dependent quadratic couplings, arbitrary Gaussian initial states, and a variety of background spacetimes. As a first set of concrete results, we prove non-perturbatively--and without invoking Bogoliubov transformations--that an accelerated detector in a cavity evolves to a state that is very nearly thermal with a temperature proportional to its acceleration, allowing us to discuss the universality of the Unruh effect. Additionally we quantitatively analyze the problems of considering single-mode approximations in cavity field theory and show the emergence of causal behaviour when we include a sufficiently large number of field modes in the analysis. Finally, we analyze how the harmonic particle detector can harvest entanglement from the vacuum. We also study the effect of noise in time dependent problems introduced by suddenly switching on the interaction versus ramping it up slowly (adiabatic activation).