Fig. 4. Enhancement of dipole-forbidden electric multipole transitions.

a Transition frequencies considered in b–e (dashed blue) and f–i (dashed green) relative to the plasmon (red) and light-line (dotted black) dispersion. b Multipolar transition rates, ${\mathrm{\Gamma }}_{\mathrm{E}n}$, associated with the 6{p, d, f, g, h} $\to \mathrm{2s}$ series of transitions in hydrogen ($\hslash {\omega }_0=\mathrm{3.02}\mathrm{eV}$). The dashed gray horizontal line marks the free-space E1 rate. The inset shows the relative rates, ${\mathrm{\Gamma }}_{\mathrm{E}n}∕{\mathrm{\Gamma }}_{\mathrm{E}n}^{\mathrm{cl}}$. c–e Differential rates $\mathrm{d}{\mathrm{\Gamma }}_{\mathrm{E}n}∕\mathrm{d}u$ [integrand of Eq. (8)] for various atom–surface separations: $h_1=\mathrm{10}\mathrm{nm}$, $h_2=\mathrm{5}\mathrm{nm}$, and $h_3=\mathrm{2.5}\mathrm{nm}$. f–i Equivalents of b–e but at the transition frequency ${\omega }_0=0.97{\omega }_{\mathrm{p}}∕\sqrt{2}$. Dotted lines indicate regions where our nonclassical framework is pushed beyond its range of validity (identified heuristically as cases where contributions to ${\mathrm{\Gamma }}_{\mathrm{E}n}$ from $q_{\mathrm{th}}\mathrm{Re}{d}_{\perp }\ge 1∕3$ exceeds 10%).