Fig. 6. Nonclassical corrections to two-photon emission enhancement.

a Two-photon emission ($\mathrm{s}\to \mathrm{s}$ transition) of a hydrogenic atom above a planar air–metal interface. b Differential decay rate in free-space for the $2\mathrm{s}\to 1\mathrm{s}$ two-photon transition in hydrogen. c, d Enhancement of the differential decay rate $\mathrm{d}{\mathrm{\Gamma }}_{\mathrm{TPE}}∕\mathrm{d}\omega$, Eq. (10), as a function of frequency for different emitter–interface separations at a transition frequency of ${\omega }_0=1.2{\omega }_{\mathrm{p}}$ ($1.4{\omega }_{\mathrm{p}}$). e Enhancement of the integrated two-photon decay rate ${\mathrm{\Gamma }}_{\mathrm{TPE}}$, as a function of transition frequency and emitter–surface separation.