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arXiv:2607.01495 · Physical Review A

Lamb Shift of a Static Atom Facing a Rotating Surface

César D. Fosco, Fernando C. Lombardo, Francisco D. Mazzitelli

quant-phcond-mat.otherhep-thSubmitted Jul 1, 2026• Announced Jul 3, 2026• 0 citations• Revised Sep 23, 2026 (v2)
v1 · Jul 1, 2026v2 · Sep 23, 2026
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Abstract

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.

Journal reference
Phys. Rev. A 114, 032823 (2026)
Comments
22 pages, 2 figures

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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 aaa. 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 ΩΩΩ, we identify two independent contributions associated with the orbital and spin components of the electromagnetic angular momentum. The orbital contribution, proportional to (Ωρ)2(Ωρ)^2(Ωρ)2, reproduces locally the Lamb shift induced by a surface translating at the tangential velocity ΩρΩρΩρ, whereas the spin contribution, proportional to (aΩ)2(aΩ)^2(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/a1/a1/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 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.
The motion of a particle in vacuum near macroscopic bodies gives rise to a Magnus-like contribution to the nonequilibrium Casimir-Polder force. This effect originates from the interplay between particle dynamics and material-modified electromagnetic quantum fluctuations, inducing in the particle a direction-dependent angular momentum coupled to the electromagnetic field spin. The resulting drift force is proportional to the cross product of the particle's angular and translational velocities, revealing a rotational transport component in the nonequilibrium Casimir-Polder interaction. Our results establish a striking connection between quantum fluctuations-induced forces and the classical Magnus effect in fluid dynamics.
We describe how the interatomic potential, or equivalently the so-called cooperative Lamb shift for a system of two identical atoms, is modified when the system is situated near metallic surfaces. For a special configuration of the atomic dipoles at a fixed distance RRR, we obtain closed analytical expressions of the potential as a function of RRR as well as the distance ZZZ of the system from a perfectly conducting surface. The potential for the same configuration is also calculated with the perfect conductor replaced by a semi-infinite electron plasma. In this case the potential gains additional contributions from the surface plasmons as well as from photon modes partially transmitted into the plasma. The surface-plasmon contribution contains an exponential function decreasing with respect to ZZZ and is consequently significant only close to the surface of the plasma. The treatment is fully quantum mechanical.
The Casimir-Polder (CP) effect -- the force between a neutral atom and an uncharged conducting plate in empty space -- is an intriguing consequence of quantum vacuum fluctuations. The typically attractive CP potential crosses over from a scaling of z−3z^{-3}z−3 at short separations to z−4z^{-4}z−4 at long distances, where retardation effects due to the finite speed of light become important. At intermediate distances, where the atom--surface separation is of the order of the wavelength of the dominant atomic transition, experiments have so far relied on indirect methods, such as diffraction or quantum reflection, to observe the CP effect. Here, we directly reveal the CP force between strontium atoms and a dielectric surface via the induced shifts in the atomic energy levels in the intermediate regime. We spectroscopically probe the CP-induced kHz-frequency shift of ultracold atoms confined by a magic-wavelength optical lattice at 189(2)~nm from the surface -- on the scale of the dominant 461-nm transition. Our measurements agree well with QED calculations and differ from the short-range approximation, while excluding the long-distance one. This paves the way for studying the CP effect across various surface properties and geometries, as well as exploring the tensor nature of the atom-surface potential -- all important for the development of hybrid atomic optical-magnetic quantum devices.
Casimir-Polder interactions cause energy and momentum exchange between microscopic and macroscopic bodies, a process mediated by quantum fluctuations in the coupled matter-electromagnetic field system. The dynamics of such effects are yet to be experimentally investigated due to the dominance of static effects at currently attainable atomic velocities. However, Y. Guo and Z. Jacob [Opt. Express 22, 26193 (2014)] have proposed a nonstatic two-plate setup where quantum-fluctuation-mediated effects have a strong velocity-dependent resonance, leading to a giant friction force on the plates. Here a more easily realizable setup, a moving atom between two stationary plates, is analyzed within a QED framework to establish the spectroscopic Casimir-Polder effects on the atom and their velocity dependence. While no large velocity-dependent enhancement is found, expressions for the plate-induced spectroscopic effects on the atom were found and further shown to be equivalent to the Doppler-shifted static result within certain velocity constraints. A numerical analysis investigates the behavior of this system for the well-studied case of the $6{D}_{3/2}\ensuremath{\rightarrow}7{P}_{1/2}$ transition in 133Cs^{133}\mathrm{Cs}133Cs interacting with sapphire plates.
This thesis focuses on theoretical quantum optics, with special emphasis on developing protocols in which engineered vacuum forces enable one to construct hybrid systems. In these systems, atoms are combined with solid-state devices in order to take advantage of their unique properties such as long coherence times of atoms and flexibility, tunability, scalability, and fast response offered by solid-state systems. Special attention is given to the study of atom-surface interactions with Rydberg atoms, where exact Fano-type diagonalization of the interaction Hamiltonian is obtained showing that, not only do Rydberg atoms suffer energy shifts, the presence of a surface leads to an alteration and admixture of the unperturbed eigenstates. Of particular interest are dispersion forces on graphene systems. We investigate whether and under which circumstances the Casimir-Polder potential between an atom and a graphene-substrate system is dominated by the interaction with graphene such that the effect of the substrate does not play an important role. We also explore the possibility to create a setup where dispersion forces could be use to bend a graphene sheet. Placing an atom close, at distances of a few hundred nanometers, to a free-standing graphene membrane we show that temporal changes in the atomic state change the Casimir-Polder interaction, thereby leading to the creation of a backaction force in the graphene sheet. Finally, we look at nonlinear atom--surface coupling processes with the aim of proposing a hybrid quantum circuit device in which individual field-excitations can be transferred between atoms and surface polaritons on demand. Deeper investigations of nonlinear processes reveal the existence of a sum rule for two-photon spontaneous decay rates that can be simply understood as a redistribution of photonic modes across the frequency spectrum where the total integrated number of modes is still conserved.