Sudden and adiabatic approximations in the excitation of a quasi-continuum

We study the coupling of a single initially occupied level to a quasi-continuum (QC) by a smoothly switched field. In the weak-field limit the dynamics is solved for an infinite, uniform, and flat QC by using perturbation theory. For a field switched on well before the recurrence time of the QC we find the peculiar ratelike time development of the sudden approximation with small modifications. For a slower turn-on we obtain an adiabatic excitation of the QC levels accompanied by quadratic and periodic oscillations of the initial state population. In the strong-field limit we find that the population recurrences of the sudden approximation gradually disappear when the turn-on time is increased. In the very-strong-field limit we demonstrate that this leads to the possibility of the adiabatic population inversion.