Time dependences of two-, three-, and four-photon ionization of atomic hydrogen in the ground1S2and metastable2S2states

Abstract

The two-level model of multiphoton ionization is reviewed within the context of an exact theoretical framework. Parametrization of the complex dressed states arising in a generalized Floquet analysis gives numerical values for the effective two-level parameters for two-, three-, and four-photon ionization of ground-state atomic hydrogen with the (${m}_{l}=0$) intermediate resonant states $2p$, $2s$, and $3p$, respectively. Detailed time dependences of the ionization process are given for responses to a linearly polarized, monochromatic, single-mode laser turned on suddenly with respect to near-resonant states, but adiabatically with respect to all others. Appropriate expressions for time-independent ionization rates are obtained during specific time intervals. The $K$ index ($K=\frac{\ensuremath{\partial}\mathrm{ln}N}{\ensuremath{\partial}\mathrm{ln}I}$), of interest in recent experiments, is understood within the framework of a simple model. Application to four-photon ionization of the metastable $^{2}S_{\frac{1}{2}}$ state of hydrogen illustrates the breakdown of the two-level model, as the number of "near-resonant" levels is a function of the field strength.