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arXiv:2308.11698 · Physical review. D/Physical review. D.

Particle detectors from localized quantum field theories

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

Published Feb 21, 2024• 22 citations
arXivHTMLPDF

Abstract

We present a fully relativistic model for localized probes in quantum field theory. Furthermore, we show that it is possible to obtain particle detector models from localized quantum field theories that interact with a free quantum field. In particular, a particle detector model is obtained when one traces out over inaccessible degrees of freedom of the localized field. This gives rise to a particle detector model, that is, a quantum degree of freedom that couples to a free field theory in an extended region of spacetime. Moreover, we show that the predictions of traditional particle detector models and fully relativistic localized fields completely coincide to leading order in perturbation theory.

DOI
10.1103/physrevd.109.045013

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We present a fully relativistic model for localized probes in quantum field theory. Furthermore, we show that it is possible to obtain particle detector models from localized quantum field theories that interact with a free quantum field. In particular, a particle detector model is obtained when one traces out over inaccessible degrees of freedom of the localized field. This gives rise to a particle detector model, that is, a quantum degree of freedom that couples to a free field theory in an extended region of spacetime. Moreover, we show that the predictions of traditional particle detector models and fully relativistic localized fields completely coincide to leading order in perturbation theory.
Using the Schwinger-Keldysh path integral, we draw a connection between localized quantum field theories and more commonly used models of local probes in relativistic quantum information (RQI). By integrating over and then tracing out the inaccessible modes of the localized field being used as a probe, we show that, at leading order in perturbation theory, the dynamics of any finite number of modes of the probe field is exactly that of a finite number of harmonic-oscillator Unruh-DeWitt (UDW) detectors. The equivalence is valid for a rather general class of input states of the probe-target field system, as well as for any arbitrary number of modes included as detectors. The path integral also provides a closed-form expression which gives us a systematic way of obtaining the corrections to the UDW model at higher orders in perturbation theory due to the existence of the additional modes that have been traced out. This approach vindicates and extends a recently proposed bridge between detector-based and field-theory-based measurement frameworks for quantum field theory [T. R. Perche et al., Particle detectors from localized quantum field theories, Phys. Rev. D 109, 045013 (2024).], and also points to potential connections between particle detector models in RQI and other areas of physics where path integral methods are more commonplace---in particular, the Wilsonian approach to the renormalization group and effective field theories.
We study the protocol of entanglement harvesting when the particle detectors that harvest entanglement from the field are replaced by fully relativistic quantum field theories. We show that two localized modes of the quantum field theories are able to harvest the same amount of leading order entanglement as two nonrelativistic particle detectors, thus implying that quantum field theoretical probes can generally harvest more entanglement than particle detectors. These results legitimize the use of particle detectors to study entanglement harvesting regardless of their internally nonrelativistic nature.
Abstract We present a framework to study the entanglement structure of a quantum field theory inspired by the formalism of particle detectors in relativistic quantum information. This framework can in principle be used to faithfully capture entanglement in a QFT between arbitrary-shaped regions of spacetime without encountering UV divergences, bypassing many of the issues typically present in other approaches. Our results also establish the limits of the efficiency of entanglement harvesting, and may also be used to motivate an operational definition of entanglement between spacetime subregions in field theory.
The paper deals with a recent systematic study of the propagation of relativistic quantum particles in spacetime. This study was a reaction to the overwhelming number of experiments dealing with the localization of not only massive but also of photons by detectors. The method of study is based on a configuration unitarity expansion of the vacuum-to-vacuum transition amplitudes as, massive and massless, particles propagate between emitters and detectors. Topics treated are the amplitudes of propagation from one time-space coordinate to another, limiting velocities of particles and their reconciliations with relativity, emergence of particles into cones in detection regions versus the direction of their moments, stimulated emissions by external sources in spacetime, scattering theory in quantum field theory in configuration space, and finally a spacetime for mulation of closed-time path for multi-particle states.
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.
Does the measurement of a quantum system necessarily break Lorentz invariance? We present a simple model of a detector that measures the spacetime localization of a relativistic particle in a Lorentz invariant manner. The detector does not select a preferred Lorentz frame as a Newton-Wigner measurement would do. The result indicates that there exists a Lorentz invariant notion of quantum measurement and sheds light on the issue of the localization of a relativistic particle. The framework considered is that of single-particle mechanics as opposed to field theory. The result may be taken as support for the interpretation postulate of the spacetime-states formulation of single-particle quantum theory.