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arXiv:2606.31752 · Physical Review Research

Signatures of the circular Unruh effect in electric and magnetic dipole transitions of multilevel atoms

Gregor Janson, Fabio Di Pumpo, Lorenz Thoma, Maxim A. Efremov

quant-phSubmitted Jun 30, 2026• Announced Jul 1, 2026• 0 citations
v1 · Jun 30, 2026v2 · Oct 12, 2026
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Abstract

The circular Unruh effect is the excitation of a detector moving along a planar circular trajectory within an electromagnetic vacuum. We demonstrate that the magnetic dipole transitions in an atom, acting as the detector, dominate the electric dipole transitions. Our analysis of both free-space and cavity schemes shows that the sensitivity to the circular Unruh effect can be maximized by balancing the minimization of mode volume against the resulting decrease in mode density. Moreover, we propose a novel measurement scheme that uses the atom's multilevel structure to suppress the spontaneous emission rate, thereby enabling the experimental detection of the circular Unruh effect.

Journal reference
Phys. Rev. Res. 8, 043029 (2026)
DOI
10.1103/6pz4-wncx
Comments
11 pages, 5 figures, 1 table

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The circular Unruh effect is the excitation of a detector moving along a planar circular trajectory within an electromagnetic vacuum. We demonstrate that the magnetic dipole transitions in an atom, acting as the detector, dominate the electric dipole transitions. Our analysis of both free-space and cavity schemes shows that the sensitivity to the circular Unruh effect can be maximized by balancing the minimization of mode volume against the resulting decrease in mode density. Moreover, we propose a novel measurement scheme that uses the atom's multilevel structure to suppress the spontaneous emission rate, thereby enabling the experimental detection of the circular Unruh effect.
We give a general treatment of the spontaneous excitation rates and the non-relativistic Lamb shift of constantly accelerated multilevel atoms as a model for multilevel detectors. Using a covariant formulation of the dipole coupling between the atom and the electromagnetic field we show that new Raman-like transitions can be induced by the acceleration. Under certain conditions these transitions can lead to stable ground and excited states that are not affected by the noninertial motion. The magnitude of the Unruh effect is not altered by multilevel effects. Both the spontaneous excitation rates and the Lamb shift are not within the range of measurability.
We propose a scheme to detect the Unruh effect in a circularly rotated Unruh-DeWitt detector enclosed within a cylindrical cavity. This technique relies on the enhanced atomic spontaneous emission rate related to the counter-rotating coupling between the detector and massless scalar fields. Our analysis demonstrates that the integration of a cylindrical cavity, coherent light excitation, and multiatom superradiation significantly enhances the signal strength, as the radiation rate associated with the standard rotating-wave coupling can be greatly suppressed within the cavity. Compared to linear acceleration, circular motion can significantly reduce the atomic acceleration path length, leading to increased detection efficiency and lower experimental difficulty. Our method provides an avenue for exploring relativistic effects on a compact, tabletop platform.
The Unruh effect predicts that accelerated observers perceive the inertial vacuum as populated by particles, providing a flat-spacetime analogue of Hawking radiation. Its direct observation, however, remains experimentally challenging, since an Unruh temperature of 1 K1\,\mathrm{K}1K requires accelerations of order 1020 m/s210^{20}\,\mathrm{m/s^2}1020m/s2. Here, we show that the Lamb shift of a centripetally accelerated atom inside a high-QQQ cavity provides a sensitive spectroscopic probe of the Unruh effect at dramatically lower accelerations. The cavity reshapes the electromagnetic density of states and converts otherwise tiny noninertial corrections into tunable level shifts. Depending on the atomic angular velocity and cavity detuning, the Lamb shift can be enhanced, strongly quenched, or completely screened. Remarkably, for experimentally realistic parameters, a rotation-induced shift of order 10  Hz10\;\mathrm{Hz}10Hz can arise already at accelerations as low as 0.5 m/s20.5\,\mathrm{m/s^2}0.5m/s2, more than twenty orders of magnitude below the acceleration scale conventionally associated with direct Unruh detection. These results identify cavity-controlled Lamb-shift spectroscopy as a viable route toward laboratory tests of the circular Unruh effect in the ultralow-acceleration regime.
We investigate the transition rates of a centripetally accelerated atom inside a high-quality cavity and show that they can be extensively tuned by adjusting the cavity resonance and the rotation frequency. Crucially, while inertial atoms cannot be excited in vacuum, rotation induces spontaneous excitation via the circular Unruh effect, with the cavity serving only as an amplifier. Using experimentally feasible parameters, we demonstrate that, in one scenario, the excitation rate can reach ∼10^{7} s^{-1} while emission remains negligible, enabling substantial population inversion. In another scenario, both excitation and emission can simultaneously attain ∼10^{7} s^{-1}, corresponding to millions of transitions per second for a single atom. These findings highlight a powerful method for manipulating atomic transition rates for quantum applications and open a promising route toward experimental verification of the circular Unruh effect with state-of-the-art quantum technologies.
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.
Quantum simulators based on Bose-Einstein condensates (BECs) provide a powerful platform to study relativistic quantum-field phenomena in the lab and in particular emulate relativistic analog particle detectors. However, such detectors typically couple to excitations beyond the acoustic phonon regime, so that the nonlinear Bogoliubov dispersion introduces corrections that cause the effective relativistic description to break down. We propose to overcome this limitation using an intrinsically momentum-selective Unruh-DeWitt detector model in which a tweezer-trapped atom couples to the condensate through a multimode optical cavity. Although the atom is effectively pointlike, the cavity-mediated interaction kernel causes it to sample density fluctuations over a controllable finite region of the BEC equivalent to a finite-size detector. The effective detector size is tunable via the cavity mode structure determining a controllable momentum cutoff that filters out nonphononic excitations. We analytically calculate the response of such a detector for uniform linear acceleration and uniform circular motion and show that this momentum selectivity can enhance the signal at experimentally accessible accelerations. Compatible with existing cavity-QED platforms our scheme thus provides a versatile setting for analog quantum-field measurements or relativistic quantum-information protocols.