Lamb Shift of a Static Atom Facing a Rotating Surface

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) squared, reproduces locally the Lamb shift induced by a surface translating at the tangential velocity Ωρ, whereas the spin contribution, proportional to (aΩ) squared, 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.