- Open Access
Signatures of the circular Unruh effect in electric and magnetic dipole transitions of multilevel atoms
Phys. Rev. Research 8, 043029 – Published 9 October, 2026
DOI: https://doi.org/10.1103/6pz4-wncx
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 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.
Physics Subject Headings (PhySH)
Article Text
References (59)
- M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, PA, 1995).
- C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973).
- R. M. Wald, General Relativity (Chicago University Press, Chicago, IL, 1984).
- L. Parker, Quantized fields and particle creation in expanding universes. I, Phys. Rev. 183, 1057 (1969).
- S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975).
- N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, 1982).
- S. A. Fulling, Nonuniqueness of canonical field quantization in Riemannian space-time, Phys. Rev. D 7, 2850 (1973).
- P. C. W. Davies, Scalar production in Schwarzschild and Rindler metrics, J. Phys. A: Math. Gen. 8, 609 (1975).
- W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D 14, 870 (1976).
- M. O. Scully, A. A. Svidzinsky, and W. Unruh, Causality in acceleration radiation, Phys. Rev. Res. 1, 033115 (2019).
- V. Sudhir, N. Stritzelberger, and A. Kempf, Unruh effect of detectors with quantized center of mass, Phys. Rev. D 103, 105023 (2021).
- J. R. Letaw, Stationary world lines and the vacuum excitation of noninertial detectors, Phys. Rev. D 23, 1709 (1981).
- L. C. B. Crispino, A. Higuchi, and G. E. A. Matsas, The Unruh effect and its applications, Rev. Mod. Phys. 80, 787 (2008).
- J. Bell and J. Leinaas, Electrons as accelerated thermometers, Nucl. Phys. B 212, 131 (1983).
- S. Hacyan and A. Sarmiento, Vacuum energy of the electromagnetic field in a rotating system, Phys. Lett. B 179, 287 (1986).
- J. Bell and J. Leinaas, The Unruh effect and quantum fluctuations of electrons in storage rings, Nucl. Phys. B 284, 488 (1987).
- S. K. Kim, K. S. Soh, and J. H. Yee, Zero-point field in a circular-motion frame, Phys. Rev. D 35, 557 (1987).
- O. Levin, Y. Peleg, and A. Peres, Unruh effect for circular motion in a cavity, J. Phys. A: Math. Gen. 26, 3001 (1993).
- J. Audretsch, R. Müller, and M. Holzmann, Generalized Unruh effect and Lamb shift for atoms on arbitrary stationary trajectories, Clas. Quantum Gravity 12, 2927 (1995).
- P. C. W. Davies, T. Dray, and C. A. Manogue, Detecting the rotating quantum vacuum, Phys. Rev. D 53, 4382 (1996).
- W. Unruh, Acceleration radiation for orbiting electrons, Phys. Rep. 307, 163 (1998).
- H. C. Rosu, Quantum vacuum radiation and detection proposals, Int. J. Theor. Phys. 44, 493 (2005).
- K. Lochan, H. Ulbricht, A. Vinante, and S. K. Goyal, Detecting acceleration-enhanced vacuum fluctuations with atoms inside a cavity, Phys. Rev. Lett. 125, 241301 (2020).
- N. Arya and S. K. Goyal, Lamb shift as a witness for quantum noninertial effects, Phys. Rev. D 108, 085011 (2023).
- Y. Zhou, J. Hu, and H. Yu, Significant circular Unruh effect at small acceleration, Phys. Rev. D 111, L041702 (2025).
- H.-T. Zheng, X.-F. Zhou, G.-C. Guo, and Z.-W. Zhou, Enhancing analog Unruh effect via superradiance in a cylindrical cavity, Phys. Rev. Res. 7, 013027 (2025).
- L. J. A. Parry and J. Louko, Connecting the circular and drifted Rindler Unruh effects, Phys. Rev. D 111, 025012 (2025).
- J. R. Letaw and J. D. Pfautsch, Quantized scalar field in rotating coordinates, Phys. Rev. D 22, 1345 (1980).
- S. Biermann, S. Erne, C. Gooding, J. Louko, J. Schmiedmayer, W. G. Unruh, and S. Weinfurtner, Unruh and analogue Unruh temperatures for circular motion in and dimensions, Phys. Rev. D 102, 085006 (2020).
- S.-Y. Zhu and M. O. Scully, Quantum interference effects in the Autler-Townes spontaneous spectrum, Phys. Lett. A 201, 85 (1995).
- M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
- C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom–Photon Interactions: Basic Processes and Applications (John Wiley & Sons, Ltd, New York, 1998).
- W. P. Schleich, Quantum Optics in Phase Space (Wiley‐VCH, Berlin, 2001).
- H. B. G. Casimir and D. Polder, The influence of retardation on the London-van der Waals forces, Phys. Rev. 73, 360 (1948).
- S. K. Lamoreaux, The Casimir force: Background, experiments, and applications, Rep. Prog. Phys. 68, 201 (2005).
- S. Y. Buhmann, Dispersion Forces I. Macroscopic Quantum Electrodynamics and Ground-State Casimir, Casimir–Polder and van der Waals Forces (Springer, Berlin, 2013).
- D. A. Steck, Quantum and atom optics (2007), http://steck.us/teaching.
- E. A. Alden, K. R. Moore, and A. E. Leanhardt, Two-photon optical clock, Phys. Rev. A 90, 012523 (2014).
- E. Alden, A two-photon E1-M1 optical clock, Ph.D. thesis, The University of Michigan, 2014.
- P. K. Schwartz and D. Giulini, Post-Newtonian Hamiltonian description of an atom in a weak gravitational field, Phys. Rev. A 100, 052116 (2019).
- P. K. Schwartz, Post-Newtonian description of quantum sys- tems in gravitational fields, Ph.D. thesis, Gottfried Wilhelm Leibniz Universität Hannover, 2020.
- G. Janson, Doppler-free two-photon transitions in atom interferometry, Master's thesis, Ulm University, 2022.
- G. Janson, A. Friedrich, and R. Lopp, Finite pulse-time effects in long-baseline quantum clock interferometry, AVS Quantum Sci. 6, 024403 (2024).
- G. Janson and R. Lopp, General relativistic center-of-mass coordinates for composite quantum particles, Phys. Rev. D 111, 064005 (2025).
- N. Funai, J. Louko, and E. Martín-Martínez, vs : Gauge invariance in quantum optics and quantum field theory, Phys. Rev. D 99, 065014 (2019).
- K. Kakazu and Y. S. Kim, Quantization of electromagnetic fields in a circular cylindrical cavity, Prog. Theor. Phys. 96, 883 (1996).
- J. Ströhle and R. Lopp, Dimensional reduction in quantum optics, Phys. Rev. Res. 6, 013285 (2024).
- I. I. Rabi, Space quantization in a gyrating magnetic field, Phys. Rev. 51, 652 (1937).
- F. J. Dyson, The radiation theories of Tomonaga, Schwinger, and Feynman, Phys. Rev. 75, 486 (1949).
- W. E. Lamb and R. C. Retherford, Fine structure of the hydrogen atom by a microwave method, Phys. Rev. 72, 241 (1947).
- H. A. Reich, J. W. Heberle, and P. Kusch, Hyperfine structure of the metastable deuterium atom, Phys. Rev. 104, 1585 (1956).
- T. F. Gallagher, Rydberg Atoms, Cambridge Monographs on Atomic, Molecular and Chemical Physics (Cambridge University Press, Cambridge, 1994).
- R. Cardman and G. Raithel, Hyperfine structure of Rydberg states in , Phys. Rev. A 106, 052810 (2022).
- I. Lesanovsky and W. von Klitzing, Time-averaged adiabatic potentials: Versatile matter-wave guides and atom traps, Phys. Rev. Lett. 99, 083001 (2007).
- S. Pandey, H. Mas, G. Drougakis, P. Thekkeppatt, V. Bolpasi, G. Vasilakis, K. Poulios, and W. von Klitzing, Hypersonic Bose–Einstein condensates in accelerator rings, Nature (London) 570, 205 (2019).
- L. S. Brown and G. Gabrielse, Geonium theory: Physics of a single electron or ion in a Penning trap, Rev. Mod. Phys. 58, 233 (1986).
- X. Fan, T. G. Myers, B. A. D. Sukra, and G. Gabrielse, Measurement of the electron magnetic moment, Phys. Rev. Lett. 130, 071801 (2023).
- Y. Jin, J. Yan, S. J. Rahman, J. Li, X. Yu, and J. Zhang, 6 GHz hyperfast rotation of an optically levitated nanoparticle in vacuum, Photonics Res. 9, 1344 (2021).
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th Dover printing, 10th GPO printing (Dover, New York, 1964).