Formation dynamics of the radial-angular structure of the Rydberg wave-packet in a resonant microwave field.

We discuss a very interesting experiment by H. Maeda, T. F. Gallagher, PRL 92, 133004 (2004), in which Li Rydberg atoms were exposed to an action of a resonant microwave filed (switched-on at $t=0$). Then, in a varying time $t_0$, the atoms were ionized by a strong sub-picosecond Half-Cycle Pulse. The probability of ionization $w_i$ was measured in its dependence on $t_0$ and the function $w_i(t_0)$ was found to be oscillating with the classical Rydberg-atom Kepler period. The original author's explanation of this effect was based on the assumption that the resonant microwave field provided formation of a localized Rydberg wave packet moving along the classical Kepler trajectory and responsible for the observed periodical dependence of $w_i(t_0)$. We suggest here an alternative interpretation of this result. By solving exactly the initial-value problem for a Rydberg atom in a microwave field we find that such a field does not provide any radial localization of a wave packet. On the other hand, it provides a rather efficient repopulation of the resonant Rydberg levels with high values of the angular momentum quantum number $l$. Migration of population to high-$l$ states is shown to cause a modulation of both angular and radial motion of a Rydberg electron. Such a periodical modulation of the electron motion is believed to provide a proper explanation of the experimental results by Maeda and Gallagher.