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arXiv:2607.03468

Superposed circular motion Unruh effect in (3+1) dimensions

Taylor Cey, Cisco Gooding, Robert Mann

quant-phmath-phSubmitted Jul 3, 2026• Announced Jul 6, 2026
arXivHTMLPDF

Abstract

Using a recently-introduced quantum control model for Unruh-DeWitt detectors in superpositions of classical trajectories, we investigate the response of a detector interacting with a massless scalar quantum field in (3+1) dimensions along a superposition of circular trajectories. We present numerical results for the transition probability and effective temperature of such a detector in four distinct geometric scenarios: (a) concentric, vertically-stacked trajectories, (b) planar, horizontally-displaced trajectories, (c) static central point and surrounding circular trajectory, and (d) concentric, planar circular trajectories. For Gaussian switching functions that are much broader than the acceleration timescale, in case (a) we find only minor deviations from the well-known, effectively thermal response of a single circular trajectory, whereas in case (c) we find a significant reduction in the effective temperature and greater variation with energy gap. We conclude with a discussion of a potential analogue implementation in ultracold atom systems.

Comments
17 pages, 16 figures

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Using a recently-introduced quantum control model for Unruh-DeWitt detectors in superpositions of classical trajectories, we investigate the response of a detector interacting with a massless scalar quantum field in (3+1) dimensions along a superposition of circular trajectories. We present numerical results for the transition probability and effective temperature of such a detector in four distinct geometric scenarios: (a) concentric, vertically-stacked trajectories, (b) planar, horizontally-displaced trajectories, (c) static central point and surrounding circular trajectory, and (d) concentric, planar circular trajectories. For Gaussian switching functions that are much broader than the acceleration timescale, in case (a) we find only minor deviations from the well-known, effectively thermal response of a single circular trajectory, whereas in case (c) we find a significant reduction in the effective temperature and greater variation with energy gap. We conclude with a discussion of a potential analogue implementation in ultracold atom systems.
Unruh-deWitt detectors have been utilized widely as probes for quantum particles, entanglement and spacetime curvature. Here, we extend the standard treatment of an Unruh-deWitt detector interacting with a massless, scalar field to include the detector traveling in a quantum superposition of classical trajectories. We derive perturbative expressions for the final state of the detector, and show that it depends on field correlation functions evaluated locally along the individual trajectories, as well as nonlocally between the superposed trajectories. By applying our general approach to a detector traveling in a superposition of two uniformly accelerated trajectories, including those with equal and differing proper accelerations, we discover novel interference effects in the emission and absorption spectra. These effects can be traced to causal relations between the superposed trajectories. Finally, we show that in general, such a detector does not thermalize even if the superposed paths would individually yield the same thermal state.
We study the properties of the transition probability and entanglement harvesting phenomenon for circularly accelerated detectors locally interacting with massless scalar fields. The dependence of the transition probability on the parameters associated with the circular motion is first analyzed in detail. By a cross-comparison with the situation of the uniformly accelerated motion, we obtain that the transition probability and the possible thermalization behavior for detectors rotating with an extremely large circular radius are analogous to that for uniformly accelerated detectors, but for a very small linear speed and a large acceleration, the effective temperature which characterizes the detectors' thermalization in a finite duration is much lower than that for uniformly accelerated detectors. We then focus on the phenomenon of entanglement harvesting in two special situations of circular trajectories, i.e., the coaxial rotation and the mutually perpendicular axial rotation by examining the concurrence as the entanglement measure in detail. We find that when two circularly accelerated detectors have equivalent acceleration and size of circular trajectory, the harvested entanglement rapidly decays with increasing acceleration or separation between two detectors. In contrast with the situation of uniform acceleration, the angular velocity would have significant impacts on entanglement harvesting. Especially for those detectors circularly moving in different directions, both the acceleration and trajectory radius play an important inhibiting role in entanglement harvesting. When two circularly accelerated detectors have different values of acceleration or angular velocity, we find that the entanglement can still be extracted by such detectors, even in the situation that one detector is at rest and the other is in a circular motion.
Abstract The Unruh effect predicts an astonishing phenomenon that an accelerated detector would detect counts despite being in a quantum field vacuum in the rest frame. Since the required detector acceleration for its direct observation is prohibitively large, recent analog studies in quantum simulation platforms help in revealing various properties of the Unruh effect and thus to explore the not-yet-understood physics of quantum gravity. To further reveal the quantum aspect of the Unruh effect, analogous experimental exploration of the correlation with respect to the detector and the field, and the consequences for coherent quantum trajectories of the detector that without classical counterparts, are essential steps but currently missing. Here, we utilize a laser-controlled trapped ion to experimentally simulate an oscillating detector coupled with a cavity field. We observe joint excitation of both the detector and the field in the detector’s frame, matching with the coordinated dynamics predicted by the Unruh effect. Particularly, we simulate the detector moving in single and superposed quantum trajectories, where the latter case shows coherent interference of excitation. Our demonstration reveals properties of quantum coherent superposition of accelerating trajectories associated with quantum gravity theories that have no classical counterparts, and may offer a new avenue to investigate phenomena in quantum field theory and quantum gravity. We also show how a generalization of the method and results in this work may be beneficial for direct observation of the Unruh effect.
The Unruh-DeWitt model of particle detector is widely used to probe quantum effects in noninertial frames and curved spacetimes. In this paper, we investigate the entanglement dynamics of a quantum system composed of two rotating Unruh-DeWitt detectors in interaction with a fluctuating massless scalar field in vacuum. We obtain the necessary and sufficient condition for the detectors to achieve steady-state entanglement, and systematically investigate the steady-state entanglement of two Unruh-DeWitt detectors rotating in coaxial orbits with the same orbital radius and angular velocity. When the separation between the detectors is vanishing, the detectors can obtain steady-state entanglement dependent on the initial state, as the detectors in uniform acceleration and static detectors in a thermal bath do. Remarkably, however, when the separation between the detectors is nonvanishing but small compared with the transition wavelength of detectors, the detectors can obtain steady-state entanglement irrespectively of what the initial state is. This is the unique phenomenon caused by the centripetal acceleration and is not present in the uniform acceleration case and the case of static detectors in a thermal bath.
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 The behavior of accelerating Unruh-DeWitt detectors coupled with a spinor field in (3+1)-dimensional spacetime is investigated. For a single point-like detector with Gaussian switching function, the transition probability increases with the acceleration and thus the antiUnruh effect effect cannot occur. Due to the spinor structure of the Dirac field, UV divergences are encountered in the calculation of the entanglement between the detectors. After introducing some UV cutoff Λ, the negativity of detectors is shown to behave nonmonotonically with respect to the acceleration. Besides, the negativity increases with the cutoff Λ and decreases with the distance between the detectors. The mutual information between the two detectors is also discussed.