In Chapters 5 – 7 we studied the onset of global chaos and its various manifestations in atomic and molecular systems. It was shown that in the kicked molecule (Section 5.4) the onset of chaos is responsible for population transfer to highly excited rotational states. A similar effect is active in microwave-driven surface state electrons and hydrogen Rydberg atoms where the onset of chaos results in strong ionization. But so far the focus has been on the computation of critical strengths and control parameters, whereas the ionization signal was reduced to play a secondary role as a probe, or an indicator for the onset of chaos. In this chapter we shift the focus to the investigation of the ionization signal itself, especially its time dependence.

The time dependence of weakly ionizing systems that are well described by a multi-photon process of order p has been studied extensively in the literature. In this case the time dependence of the ionization signal does not offer any surprises. We expect exponential decay with a decay rate ρ that is proportional to the pth power of the field intensity I according to ρ ∼ Ip. This prediction of multi-photon theory has been verified in numerous experiments. In fact, experimentalists often use the field dependence of the ionization rates to assign a multi-photon order to an experimentally observed ionization signal.