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arXiv:2604.16568

Momentum reconstruction from Unruh-deWitt detectors

Jesse Huhtala, Iiro Vilja

quant-phSubmitted Apr 17, 2026• Announced Apr 20, 2026• 0 citations
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Abstract

We investigate momentum reconstruction for particle processes observed by Unruh-deWitt detector setups. In particular, we derive the probability distributions for particle momenta conditioned on detector clicks in three spatial dimensions. We investigate the statistical properties of such detector setups and discuss their use as models of measurement devices in particle physics.

Comments
20 pages, 2 figures

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We investigate momentum reconstruction for particle processes observed by Unruh-deWitt detector setups. In particular, we derive the probability distributions for particle momenta conditioned on detector clicks in three spatial dimensions. We investigate the statistical properties of such detector setups and discuss their use as models of measurement devices in particle physics.
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.
This is the second paper on a new formalism for relativistic quantum measurements. Here, we construct a fully relativistic model for detectors that takes into account the detector's state of motion, intrinsics dynamics, initial states and couplings to the measured field. The dual classical/quantum description of the detector is implemented by using a master-equation type of approximation for the coarse-grained pointer variables. Then we identify the probabilities that correspond to ideal measurements, i.e., measurements that are largely insensitive to modeling details of the apparatus. The Unruh-Dewitt and Glauber detectors are recovered at the appropriate limits. We employ our results to models of particle detection, photodetection and relativistic spin measurements, and we derive an ideal distribution for relativistic time-of-arrival probabilities.
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.
A simple but powerful particle detector model consists of a two-level system coupled to a field, where the detected particles are the field excitations. This is known as the Unruh-DeWitt detector. Research using this model has often focused on either a completely classical description of the external degrees of freedom of the detector, or a full field-theoretic treatment, where the detector itself is described as a field. Recently there has been much interest in quantum aspects of the detector's center of mass---either described as moving in superposition along semiclassical trajectories, or dynamically evolving under a nonrelativistic Hamiltonian. However, the processes of interest---the absorption or emission of field particles---necessarily change the detector's rest mass by the amount of energy of the absorbed or emitted field quanta. Neither of the above models can capture such effects. Here we incorporate the quantization of the detector's mass-energy into the Unruh-DeWitt model. We show that internal energy changes due to emission or absorption are relevant even in the lowest energy limit. Specifically, corrections to transition rates due to the detector's mass changing cannot be ignored unless the entire center of mass dynamics is also ignored. Our results imply that one cannot have a consistent model of the Unruh-DeWitt detector as a massive particle without including the mass-energy equivalence.
We calculate the response of an Unruh--DeWitt detector in a 2+1d spacetime that contains a BTZ black hole in a superposition of locations as viewed in a reference system associated with the detector. Upon performing a Quantum Reference Frame (QRF) transformation, this can also be seen as a detector in a superposition of locations in a single classical black hole spacetime. We use this to derive the form of the interaction of the detector and scalar field in such a superposition of spacetimes, ignoring backreaction. We define a measurement whose outcome probabilities contain a nonclassical contribution that would be absent for a black hole described by a classical mixture of positions. Finally, we compare our results with a previously studied setup involving a mass-superposed black hole by Foo et al. [Phys. Rev. Lett. 129, 181301 (2022)], and highlight a key difference. We show analytically how this difference arises and find singularities in the mass-superposed spectrum probed by the detector.
Based on our results for the detector-field system in Gaussian states, I am addressing the following issues about the quantum dynamics of atoms or detectors moving in a relativistic quantum field: First, the dynamics of the detectors as an open quantum quantum system, hence the entanglement creation and sudden death processes between the detectors, are non-Markovian in general. Second, the excitations of the accelerated detectors in the Unruh effect depend only on the kinematics of the detectors. The event horizon for the detector is not essential in this effect, and the particle notion of the quantum field is not needed here. Third, entanglement dynamics of the detectors are independent of time-slicing scheme. Local projective measurements on point-like detectors are also consistent in different time-slicing schemes even in the presence of relativistic quantum fields.