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 ({~}10¹³ W/cm²) linearly polarized laser. A numerical solution of the time-dependent Schr\"odinger 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 Cₐ(t) =F_-∞^∞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}) =(α³/3{π})F_-∞^∞dt e^iΩt{C}ₐ$(t). Copious radiation, near the second harmonic, was emitted from this metastable excited state, prior to ionization.