Excitation of multilevel Rydberg states (atoms and diatomic molecules) is studied under an intense time-periodic perturbation that is instantaneously turned on and off. For a one-quantum excitation from a lower lying state, general expressions for the Laplace images of the population amplitudes of Rydberg states are obtained with regard to their decay characteristics. It is shown that the problem considered is reduced to the determination of the positions and widths of the energy levels of a quantum system in the field of monochromatic laser radiation of the same frequency and intensity as that in a pulse mode. To determine these quantities, an integral formulation is proposed for the eigenvalue problem for energies that is relatively simply solved with regard to the effect of the ionic core and its complex vibration-rotation structure on diatomic molecules. The specific features of the excitation of Rydberg states and the behavior of Rydberg wave packets are studied depending on the intensity and duration of laser radiation. A quantum phenomenon of rotational orientation of electron-excited diatomic molecules is considered.
We study, using a combination of experiment and theory, the excitation and decay of very-high-$n\phantom{\rule{4pt}{0ex}}(n\ensuremath{\sim}280\text{--}430)$ strontium autoionizing Rydberg states formed by near-resonant driving of the $5s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}5p\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2}$ core-ion transition. The branching ratio between decay through radiative transitions and through autoionization is explored. Autoionization rates are measured as a function of both the
n and $\ensuremath{\ell}$ quantum numbers of the Rydberg electron. The nonstationary decay dynamics is studied by creating and manipulating Rydberg wave packets and by varying the laser pulse that drives the core excitation.