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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Continuous measurement and localization in the Unruh effect

Jürgen Audretsch, Michael B. Mensky, Rainer Müller

Published Feb 15, 1995• 10 citations
Publisher

Abstract

We consider the influence of continuous decoherence on the excitation of an accelerated detector, an effect which must be taken into account in physically realistic realizations of the Unruh effect. As a model we use a quantum two-level system (as the detector) coupled to a massless scalar quantum field. This composite quantum system is treated as an open system which interacts with an environment so that continuous decoherence results. We develop a formalism that models the interaction with an environment approximately as a continuous measurement, represented by a sequence of state reductions. This leads to a description in terms of ``histories'' of the detector. Evolution operators corresponding to different histories of the detector can then be considered separately. The density matrix for the mixed state which results after a sequence of nonselective measurements is worked out explicitly. Based on the same formalism, it is also possible to correlate the time of the transition of the detector with the trajectories of the Minkowski particles which are emitted during this process, thus localizing the space-time region where they are created.

DOI
10.1103/physrevd.51.1716

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We consider the influence of continuous decoherence on the excitation of an accelerated detector, an effect which must be taken into account in physically realistic realizations of the Unruh effect. As a model we use a quantum two-level system (as the detector) coupled to a massless scalar quantum field. This composite quantum system is treated as an open system which interacts with an environment so that continuous decoherence results. We develop a formalism that models the interaction with an environment approximately as a continuous measurement, represented by a sequence of state reductions. This leads to a description in terms of ``histories'' of the detector. Evolution operators corresponding to different histories of the detector can then be considered separately. The density matrix for the mixed state which results after a sequence of nonselective measurements is worked out explicitly. Based on the same formalism, it is also possible to correlate the time of the transition of the detector with the trajectories of the Minkowski particles which are emitted during this process, thus localizing the space-time region where they are created.
The Unruh effect remains a central topic in quantum field theory, although its direct experimental verification continues to be challenging. Recent efforts have therefore focused on indirect detection strategies in which the Unruh effect emerges through measurable physical processes. In this work, we extend a previously introduced detector model, originally formulated for a massless scalar field, to the electromagnetic field. We show that the decoherence decay rates differ between inertial and accelerated frames. Furthermore, we demonstrate that the characteristic exponential decay associated with the Unruh effect can be observed at lower accelerations than those considered in earlier studies.
Uniform acceleration induces a thermal response to the Minkowski vacuum and can thereby modify quantum correlations. For measurement-induced nonlocality (MIN), a form of nonclassical correlation distinct from entanglement, previous field-mode analyses of bosonic fields found that it decreases with increasing acceleration and vanishes in the infinite-acceleration limit. This raises the question of whether the disappearance of MIN is a generic consequence of the Unruh effect or depends on the physical description of the accelerated quantum system. To address this question, we study two uniformly accelerating Unruh-DeWitt detectors interacting with a massless scalar field. We find that the response of MIN to the Unruh temperature depends sensitively on the initial detector state: it can decrease monotonically, vanish at an intermediate temperature and subsequently recover, or increase monotonically. Moreover, for a broad class of initial states, MIN approaches a nonzero value in the high-temperature limit. These results show that the suppression of MIN under strong acceleration is not universal. Instead, Unruh-induced detector dynamics gives rise to a state-dependent response in which measurement-induced nonlocality can be suppressed, restored, or enhanced.
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.
Abstract We study, in the framework of open quantum systems, the entanglement dynamics for a quantum system composed of two uniformly accelerated Unruh-Dewitt detectors interacting with a bath of massive scalar fields in the Minkowski vacuum. We find that the entanglement evolution for the quantum system coupled with massive fields is always slower compared with that of the one coupled with massless fields, and this time-delay effect brought about by the field being massive can however be counteracted by a large enough acceleration, in contrast to the case of a static quantum system in a thermal bath, where this time delay is not affected by the temperature. Remarkably, the maximal concurrence of the quantum system generated during evolution may increase with acceleration for any inter-detector separation while that for static ones in a thermal bath decreases monotonically with temperature, and this can be considered as an anti-Unruh effect in terms of the entanglement generated.
Abstract Recently, interest has been growing in studies on discrete or ‘pixelated’ space-time that, through modifications in the dispersion relation, can treat the vacuum as a dispersive medium. Discrete spacetime considers that spacetime has a cellular structure on the order of the Planck length, and if this is true we should certainly have observable effects. In this paper, we investigated the effects caused by the dispersive vacuum on the decoherence process of an Unruh–DeWitt detector, our setup consists of a uniformly accelerated detector, initially in a qubit state, which interacts with a massless scalar field during a time interval finite. We use dispersion relations drawn from doubly special relativity and Hořava–Lifshitz gravity, with these modifications the vacuum becomes dispersive and has a corresponding refractive index. We calculate the probability transition rates, the probability of finding the detector in the ground state, and the quantum coherence variation. Our results indicate that the decoherence process occurs more quickly in cases with changes in the dispersion relation in the regime of high accelerations and interaction time. Additionally, the decoherence increases as the vacuum becomes more dispersive due to the increase in the order of modification in the dispersion relation, and this happens because the dispersive vacuum amplifies the effects of quantum fluctuations that are captured by the detector when interacting with the field.