Radiation emitted by a resonantly driven hydrogen atom

The spectrum of scattered radiation was computed for an electron, bound initially in the 2s state of a hydrogen atom and driven resonantly by the sinusoidal field of a moderately intense (∼${10}^{13}$ W/${\mathrm{cm}}^2$) linearly polarized laser. A numerical solution of the time-dependent Schrödinger equation was performed for the duration of a 20–30-fs laser pulse. The radiation which emerges from this transient state was characterized by the autocorrelation function of the electronic acceleration defined as ${\mathit{C}}_{\mathit{a}}$(t) =${\mathcal{F}}_{\mathrm{-}\mathrm{\infty }}^{\mathrm{\infty }}$dt’〈1s‖a(t’)⋅a(t’-t)‖1s〉, as previously described [K. LaGattuta, J. Mod. Opt. 39, 1181 (1992)]. Then the energy spectrum of the radiation was determined from S(Ω) =(${\mathrm{\alpha }}^3$/3π)${\mathcal{F}}_{\mathrm{-}\mathrm{\infty }}^{\mathrm{\infty }}$dt ${\mathrm{e}}^{\mathit{i}\mathrm{\Omega }\mathit{t}}$ ${\mathit{C}}_{\mathit{a}}$(t). Copious radiation, near the second harmonic, was emitted from this metastable excited state, prior to ionization.