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 $\Omega$, we identify two independent contributions associated with the orbital and spin components of the electromagnetic angular momentum. The orbital contribution, proportional to $(\Omega\rho)^2$, reproduces locally the Lamb shift induced by a surface translating at the tangential velocity $\Omega\rho$, whereas the spin contribution, proportional to $(a\Omega)^2$, 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.