Stochastic ionization of surface-state electrons: Classical theory

In recent experimental investigations of the ionization of Rydberg atoms in low-frequency electromagnetic fields, ionization rates have been measured which depend strongly on the intensity of the oscillating fields but only weakly on the frequency. In an attempt to understand this ionization mechanism, an analogous, one-dimensional system is considered consisting of a surface-state electron bound to the surface of liquid helium by its image charge. A complete classical analysis of the behavior of this nonlinear oscillator in a microwave field is presented which shows that above a critical field strength the electron dynamics become chaotic and the electron diffuses in energy until it ionizes. Analytic estimates for the classical thresholds and rates for stochastic excitation and ionization are determined as functions of the microwave-field amplitude and frequency. Since the microwave frequencies and field strengths required for stochastic ionization of this one-dimensional "hydrogen" atom are readily available, this system provides an opportunity to thoroughly explore the manifestations of classical chaos in a quantum system.