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 decrease or increase the energy-level spacing, depending on the angular-velocity regime. In contrast, for atoms polarizable perpendicular to the rotation axis, the noninertial contribution appears already at the leading 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.
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
1K requires accelerations of order
1020m/s2. Here, we show that the Lamb shift of a centripetally accelerated atom inside a high-
Q 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
10Hz can arise already at accelerations as low as
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 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 investigate the effect of the GUP on the Lamb shift of a two-level atom interacting with a real massless scalar quantum field, within the DDC formalism. For an atom undergoing inertial motion, uniform acceleration, and uniform circular motion, we analyze the separate contributions of vacuum fluctuations and radiation reaction. We first derive the statistical functions of the field along the atom's trajectories for the three types of motion, expressing them as frequency integrals, and then employ them to calculate the vacuum fluctuation and radiation reaction contributions to the radiative level shift. We show that the GUP-modified Lamb shift of the two-level atom arises entirely from vacuum fluctuations and acquires additional corrections proportional to
β. We focus in particular on the acceleration-dependent GUP corrections. For a uniformly accelerated atom, the GUP corrections comprise thermal and nonthermal parts. At low accelerations, the thermal part exhibits nonmonotonic behavior, and is proportional to
a4 in the limit
a/ω0→0; the nonthermal part, by contrast, grows nonlinearly and monotonically, exceeding the thermal part by nearly two orders of magnitude at large accelerations. For an atom in uniform circular motion, the GUP corrections are purely nonthermal and also display a nonlinear, monotonic dependence on acceleration, increasing or decreasing steeply according to the sign of
β. For the same
β, the corrections are larger in uniform circular motion than in uniformly accelerated motion, since the former involves terms proportional to both
a2 and
a3, whereas the latter contains only
a2 terms.
We study how the Lamb shift of a static atom is modified when a nearby planar body rotates rigidly about its normal while the atom is held at a fixed distance
a. We derive a general formula for the shift in terms of the angularly Doppler-shifted reflection coefficients of the surface, valid for any axially symmetric planar material. Expanding the result to second order in the angular velocity
Ω, we identify two independent contributions associated with the orbital and spin components of the electromagnetic angular momentum. The orbital contribution, proportional to
(Ωρ)2, reproduces locally the Lamb shift induced by a surface translating at the tangential velocity
Ωρ, whereas the spin contribution, proportional to
(aΩ)2, originates from the rotational Doppler shift of the photon helicity and survives even on the rotation axis. We first illustrate the formalism using a graphene sheet and then apply it to finite-thickness Drude and plasma conductors and to doped semiconductors. Rotation enhances the Casimir-Polder interaction for graphene and metallic surfaces, whereas it weakens it for doped semiconductors, depending on whether the carrier plasma frequency reaches the near-field scale
1/a. Above a threshold angular velocity, the atomic level also acquires a finite linewidth, providing a spectroscopic signature of quantum friction. Furthermore, rotation induces a novel component of the Casimir-Polder force, which is perpendicular to both the standard normal attraction and the tangential quantum-friction force.
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.