THE IMPORTANCE OF RESONANCES IN MICROWAVE IONIZATION OF EXCITED HYDROGEN-ATOMS

What is the behavior of a low-dimensional quantal system whose classic al, deterministic, Hamiltonian, counterpart is non-integrable and unde rgoes a transition to chaos? After a general introduction this report engages the question by focussing on hydrogen atoms prepared with prin cipal quantum number n(0) much greater than 1 being driven by a linear ly polarized, periodic electric field strong enough to cause ''ionizat ion''; this means true ionization plus excitation to above an experime ntally determined n-cutoff n(c) > n(0). This is one of the few time-de pendent systems on which experiments, quantal calculations, and classi cal calculations have been done in sufficient depth to show that answe rs to the question range from simple to subtle. The dynamical behavior of the system changes with increasing scaled frequency, which classic ally is the ratio omega/omega(K) of the driving frequency omega and th e unperturbed Kepler frequency omega(K). Quantally, this corresponds t o n(0)(3) omega in atomic units. Comparisons among experimental data a nd quantal and classical theoretical calculations have so far revealed six different regimes of dynamical behavior for different ranges of n (0)(3) omega. After describing all six, this report emphasizes the fir st three, or n(0)(3) omega up to about 1.2. Described in detail are ex periments carried out at Stony Brook with n(0) = 32,...,90 hydrogen at oms being driven by an omega/2 pi = 9.92 GHz field, or n(0)(3) omega = 0.05-1.1 (subsequently extended down to n(0) = 24, or n(0)(3) omega = 0.021). The data show the quantal system being influenced by various resonance effects, some of whose origins are most easily found in the corresponding classical system, others of which are not. When omega/om ega(K) is near low-order rational fractions r/s, r = 1,2, and s = 1,2, ..., the classical dynamics is strongly affected by nonlinear resonanc es easily visualized in computed stroboscopic phase portraits of the I d motion. The trapping of orbits inside them leads to classical local stability. Where the quantitative agreement between experimental data and classical calculations is good for threshold field amplitudes for the onset of ''ionization'', the classical theory gives keen insight i nto the semiclassical dynamics. Conversely, where the quantitative agr eement breaks down is a signature for the importance of quantal effect s. Often this occurs where the nonclassical behavior is, nevertheless, stiff anchored in subtle ways to the classical dynamics in and near n onlinear resonances. The report includes a detailed, critical comparis on among data sets for n(0)(3) omega less than or equal to 1.1 obtaine d from experiments in different laboratories, using either excited hyd rogen atoms or alkali Rydberg atoms prepared in hydrogen-like states w ith small quantum defects. It also includes a careful discussion of ex perimental data obtained with a static electric field superimposed wit h the microwave electric field. The data demonstrate that the static e lectric field may be used to fine-tune the scaled frequency, which is likely to be exploited to advantage in future experiments.