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arXiv:2509.16488 · Physical review. D/Physical review. D.

Spontaneous excitation of a centripetally accelerated atom coupled to electromagnetic vacuum fluctuations near a reflecting boundary

Yan Peng, Jiawei Hu, Hongwei Yu

Published Jul 16, 2025• 2 citations
arXivHTMLPDF

Abstract

We investigate the rate of change of the mean atomic energy for centripetally accelerated atoms interacting with electromagnetic vacuum fluctuations near a reflecting boundary, using the Dalibard-Dupont-Roc-Cohen-Tannoudji formalism. The distinct contributions from vacuum fluctuations and radiation reaction are analyzed separately. Our results reveal that, when the centripetal acceleration significantly exceeds the characteristic acceleration set by the atomic transition frequency, vacuum fluctuations dominates over radiation reaction, irrespective of the atom-boundary distance and the atomic polarization. In the near-zone regime, where the atom-boundary distance is much smaller than both the characteristic length associated with the acceleration and the transition wavelength of the atom, the boundary introduces substantial corrections to the rate of change of the mean atomic energy. These corrections are comparable in magnitude to those in free space and exhibit strong dependence on the atomic polarization. Remarkably, in the intermediate and far regions, contributions stemming from the combined effects of the boundary and acceleration can become the leading and subleading terms, respectively. An acceleration-independent term also arises from their interplay. These findings highlight the significant interplay between acceleration and the presence of a boundary in shaping atomic radiative properties and may have potential implications for experimentally probing the circular Unruh effect.

DOI
10.1103/dlbb-tnjc

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We investigate the rate of change of the mean atomic energy for centripetally accelerated atoms interacting with electromagnetic vacuum fluctuations near a reflecting boundary, using the Dalibard-Dupont-Roc-Cohen-Tannoudji formalism. The distinct contributions from vacuum fluctuations and radiation reaction are analyzed separately. Our results reveal that, when the centripetal acceleration significantly exceeds the characteristic acceleration set by the atomic transition frequency, vacuum fluctuations dominates over radiation reaction, irrespective of the atom-boundary distance and the atomic polarization. In the near-zone regime, where the atom-boundary distance is much smaller than both the characteristic length associated with the acceleration and the transition wavelength of the atom, the boundary introduces substantial corrections to the rate of change of the mean atomic energy. These corrections are comparable in magnitude to those in free space and exhibit strong dependence on the atomic polarization. Remarkably, in the intermediate and far regions, contributions stemming from the combined effects of the boundary and acceleration can become the leading and subleading terms, respectively. An acceleration-independent term also arises from their interplay. These findings highlight the significant interplay between acceleration and the presence of a boundary in shaping atomic radiative properties and may have potential implications for experimentally probing the circular Unruh effect.
We study the spontaneous excitation of a uniformly accelerated two-level atom nonlinearly coupled to vacuum Dirac field fluctuations using the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji and generalized by us to the present case in the current paper. We find that a cross term involving both vacuum fluctuations and radiation reaction appears, which is absent in the linear coupling cases such as an atom interacting with vacuum scalar or electromagnetic fluctuations. Furthermore, the contribution of this term actually dominates over that of radiation reaction. Thus, the mean rate of change of the atomic energy can no longer be distinctively separated into only the contributions of vacuum fluctuations and radiation reaction as in the scalar and electromagnetic cases where the coupling is linear. Our result shows that a uniformly accelerated atom interacting with vacuum Dirac fluctuations would spontaneously excite and a unique feature in sharp contrast to the scalar and electromagnetic cases is the appearance of a term in the excitation rate, which is proportional to the quartic acceleration.
Abstract We study the average rate of change of energy of two accelerated entangled atoms coupled to electromagnetic fields in the presence of a reflecting boundary, which according to the Dalibard, Dupont–Roc and Cohen-Tannoudji formalism is only attributed to the contribution of the radiative reaction of atoms. When the boundary is present, this result can be expressed as the sum of the free-space result and the boundary-induced modifications, and it generally depends on the two-atom initial state, the orientations of atomic dipole moments, as well as the relative scales among atom-boundary distance, interatomic separation and the inverse of atomic acceleration. When the two atoms are vertically aligned and one atom is very close to the boundary, we find that the terms only related to the closer atom are zero for the symmetric state but double the free-space counterpart for the antisymmetric state, if the atom is polarizable parallel to the boundary. However, for the atom polarizable vertically to the boundary, these terms vanish for the antisymmetric state but are twice the free-space counterpart for the symmetric state. Moreover, the terms related to the farther atom exhibit obviously oscillatory behavior, and the terms related to both atoms are vanishing unless the dipole moments of two atoms both have their components vertical to the boundary. When the two atoms are aligned parallel to and very close to the boundary, the terms related to one atom are interatomic-separation-independent and only influenced by the atomic dipole moments. The terms related to both atoms are actually consistent with the counterpart in the vertical-alignment case. In addition, when the two atoms are polarizable along the direction parallel to the boundary, the average rate of change of energy of two parallel-aligned and symmetric entangled atoms vanishes as if the two atoms were a closed system.
We consider a uniformly accelerated atom interacting with a vacuum electromagnetic field in the presence of an infinite conducting plane boundary and calculate separately the contributions of vacuum fluctuations and radiation reaction to the atomic energy-level shift. We analyze in detail the behavior of the total energy shift in three different regimes of the distance in both the low-acceleration and high-acceleration limits. Our results show that, in general, an accelerated atom does not behave as if immersed in a thermal bath at the Unruh temperature in terms of the atomic energy-level shifts, and the effect of the acceleration on the atomic energy-level shifts may in principle become appreciable in certain circumstances, although it may not be realistic for actual experimental measurements. We also examine the effects of the acceleration on the level shifts when the acceleration is of the order of the transition frequency of the atom and we find some features which differ from what was obtained in the existing literature.
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.
We study the resonant dipole–dipole interaction energy between two non-inertial identical atoms, one excited and the other in the ground state, prepared in a correlated Bell-type state, and interacting with the scalar field or the electromagnetic field nearby a perfectly reflecting plate. We suppose the two atoms move with the same uniform acceleration, parallel to the plane boundary, and that their separation is constant during the motion. By separating the contributions of radiation reaction field and vacuum fluctuations to the resonance energy shift of the two-atom system, we show that Unruh thermal fluctuations do not affect the resonance interaction, which is exclusively related to the radiation reaction field. However, non-thermal effects of acceleration in the radiation-reaction contribution, beyond the Unruh acceleration–temperature equivalence, affect the resonance interaction energy. By considering specific geometric configurations of the two-atom system relative to the plate, we show that the presence of the mirror significantly modifies the resonance interaction energy between the two accelerated atoms. In particular, we find that new and different features appear with respect to the case of atoms in the free-space, related to the presence of the boundary and to the peculiar structure of the quantum electromagnetic field vacuum in the locally inertial frame. Our results suggest the possibility to exploit the resonance interaction between accelerated atoms as a probe for detecting the elusive effects of atomic acceleration on radiative processes.
We consider a multilevel hydrogen atom in interaction with the quantum electromagnetic field and separately calculate the contributions of the vacuum fluctuation and radiation reaction to the rate of change of the mean atomic energy of the atom for uniform acceleration. It is found that the acceleration disturbs the vacuum fluctuations in such a way that the delicate balance between the contributions of vacuum fluctuation and radiation reaction that exists for inertial atoms is broken, so that the transitions to higher-lying states from ground state are possible even in vacuum. In contrast to the case of an atom interacting with a scalar field, the contributions of both electromagnetic vacuum fluctuations and radiation reaction to the spontaneous emission rate are affected by the acceleration, and furthermore the contribution of the vacuum fluctuations contains a nonthermal acceleration-dependent correction, which is possibly observable.