Detectors for probing relativistic quantum physics beyond perturbation theory

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).

Extraction of genuine tripartite entanglement from the vacuum

“…(11) or (5). Note that we are assuming here Gaussian states of zeromean; extending the formalism beyond this assumption is straightforward but unnecessary here.…”

“…For more indepth information on the oscillator-detector model the reader is referred to [5]. The formalism also involves the use of Gaussian quantum mechanics; the unfamiliar reader may find many review articles on this subject, for example [12].…”

“…The authors, however, took into account only a single mode of the field that lead to problems with causality violation. The problem was fixed in [5] by adding more field modes and the idea was further developed, providing a useful formalism for the analytical treatment of point-like detectors interacting with the vacuum. This formalism has been extensively used to study various scenarios in the harvesting of entanglement [4][5][6] and more general quantum correlations [7] in the case of bipartite harvesting (i.e.…”

Casimir forces on atoms in optical cavities

“…. Force (in Newtons) due to a uniformly-distributed row of atoms (at positions xn/L = n N +1 ), compared with the value of the Casimir force as given by (32). There are two cases, which are a row of atoms with fixed relative positions xn/L, as given by (30) and the same row of atoms with positions xn fixed with respect to the plate at x = 0, given by (31).…”

“…One small caveat is that this simple model encodes the basic features of the light-matter interaction for atomic transitions only in the absence of the exchange of orbital angular momentum [18]. The model has been used in studies of Casimir-Polder forces involving only one conducting plate [19][20][21][22] and is commonly used in studies of quantum field theory in curved spacetimes and relativistic quantum information [30][31][32][33][34][35], as well as in quantum optics (see, e.g., [36]). However, the model does not contain the analog of a diamagnetic field self-interaction term as in (1).…”