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arXiv:2006.12514 · Physical review. D/Physical review. D.

Broken covariance of particle detector models in relativistic quantum information

Eduardo Martín-Martínez, Tales Rick Perche, Bruno de S. L. Torres

Published Jan 12, 2021• 64 citations
arXivHTMLPDF

Abstract

We show that the predictions of commonly used spatially smeared particle detectors coupled to quantum fields are not generally covariant outside the pointlike limit. This lack of covariance manifests itself as an ambiguity in the time-ordering operation. We analyze how the breakdown of covariance affects typical detector models in quantum field theory such as the Unruh--DeWitt model. Specifically, we show how the violations of covariance depend on the state of the detectors-field system, the shape and state of motion of the detectors, and the spacetime geometry. Furthermore, we provide the tools to explicitly evaluate the magnitude of the violation and identify the regimes where the predictions of smeared detectors are either exactly or approximately covariant in perturbative analyses, thus providing limits of validity of smeared particle detector models.

DOI
10.1103/physrevd.103.025007

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We show that the predictions of commonly used spatially smeared particle detectors coupled to quantum fields are not generally covariant outside the pointlike limit. This lack of covariance manifests itself as an ambiguity in the time-ordering operation. We analyze how the breakdown of covariance affects typical detector models in quantum field theory such as the Unruh--DeWitt model. Specifically, we show how the violations of covariance depend on the state of the detectors-field system, the shape and state of motion of the detectors, and the spacetime geometry. Furthermore, we provide the tools to explicitly evaluate the magnitude of the violation and identify the regimes where the predictions of smeared detectors are either exactly or approximately covariant in perturbative analyses, thus providing limits of validity of smeared particle detector models.
We analyze potential violations of causality in Unruh DeWitt-type detector models in relativistic quantum information. We proceed by first studying the relation between faster-than-light signaling and the causal factorization of the dynamics for multiple detector-field interactions. We show in what way spatially extended nonrelativistic detector models predict superluminal propagation of the field's initial conditions. We draw parallels between this characteristic of detector models, stemming from their nonrelativistic dynamics, and Sorkin's ``impossible measurements on quantum fields'' [R. D. Sorkin, in Directions in General Relativity: Proceedings of the 1993 International Symposium, Maryland (Cambridge University Press, 1993), Vol. 2, pp. 293--305.]. Based on these features, we discuss the validity of measurements in quantum field theory when performed with nonrelativistic particle detectors.
Pointlike systems coupled to quantum fields are often employed as toy models for measurements in quantum field theory. In this paper, we identify the field observables recorded by such models. In the case of detector models that work in the strong coupling regime, we show that the detector's pointer variable is correlated with time-extended smeared field amplitudes, and it is insensitive to the particle content of the field's state. Then, we show that detector models that work in the weak coupling regime can account for particle phenomenology, such as the existence of a particlelike time-of-arrival and resonant behavior. Finally, we develop an improved field-detector interaction model, adapting the formalism of quantum Brownian motion, that is exactly solvable. This model confirms the association of field and particle properties in the strong and weak coupling regimes, respectively. Further, it can also describe the intermediate regime, in which the field-particle characteristics ``merge.'' In contrast to standard perturbation techniques, this model also recovers the relativistic Breit-Wigner resonant behavior in the weak coupling regime. The modulation of particle-field duality by a single tunable parameter is a novel feature that is, in principle, experimentally accessible.
Unruh-DeWitt detectors interacting locally with a quantum field are systems under consideration for relativistic quantum information processing. In most works, the detectors are assumed to be pointlike and, therefore, couple with the same strength to all modes of the field spectrum. We propose the use of a more realistic detector model where the detector has a finite size conveniently tailored by a spatial profile. We design a spatial profile such that the detector, when inertial, naturally couples to a peaked distribution of Minkowski modes. In the uniformly accelerated case, the detector couples to a peaked distribution of Rindler modes. Such distributions are of special interest in the analysis of entanglement in noninetial frames. We use our detector model to show the noise detected in the Minkowski vacuum and in single particle states is a function of the detector's acceleration.
We analyze the constraints that causality imposes on some of the particle detector models employed in quantum field theory in general and, in particular, on those used in quantum optics (or superconducting circuits) to model atoms interacting with light. Namely, we show that disallowing faster-than-light communication can impose severe constraints on the applicability of particle detector models in three different common scenarios: (1) when the detectors are spatially smeared, (2) when a UV cutoff is introduced in the theory and (3) under one of the most typical approximations made in quantum optics: the rotating-wave approximation. We identify the scenarios in which the models' causal behavior can and cannot be cured.
We study a 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 and provides 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 noncausal. 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.
In this paper we analyze the problem of ``apparent'' superluminal signalling and retrocausation that can appear for particle detector models when considering noncompactly supported field-detector interactions in quantum field theory in curved spacetimes and in relativistic quantum information protocols. For this purpose, we define a signalling estimator based on an adapted version of the quantum Fisher information to perturbative regimes. This allows us to study how the internal dynamics of the detectors (for example the gap between the detector energy levels) have an impact on the ability of particle detectors to communicate with one another. Moreover, we show that, very generally, even for detectors with infinite tails in space and time, if the tails decay exponentially, one can define an effective light cone, outside of which signalling is negligible. This provides concrete evidence supporting the use of noncompact (but exponentially decaying) detector smearings in protocols of relativistic quantum information.