Quantum Systems Periodically Perturbed in Time

Abstract

In 1974, J.E. Bayfield and P.M. Koch [1] performed a puzzling experiment on microwave ionization of hydrogen atoms. A beam of hydrogen atoms in a highly excited state (typically 50≤n≤80) crosses a microwave chamber. At the end of the cavity a counter measures the ionization rate. The results shown in fig. 1 below exhibit a transition between a regime of low field amplitude where almost all atoms are stable and a regime of high field amplitude where almost all atoms are ionized. Several frequencies were used but even the highest one represents only about 1% of the photon frequency for excitation to the continuum. This means that a perturbation theory is useless since it would require at least the calculation of hundred orders, and even in this case it would give significant predictions only in a very small range of values of the field amplitude. All other methods of spectroscopy failed to explain this effect. In 1978, following a suggestion by Lamb, J.6. Leopold and I.e. Percival [2] showed from a numerical simulation, that a purely classical treatment was quite efficient in describing quantitatively the experimental datas. Following this idea, R. Jensen [3] proposed in 1982 a theoretical scheme using the classical evolution of a one dimensional hydrogen atom in order to estimate the critical field amplitude: restricting the motion to the negative energy configurations the ionization occurs when the field amplitude is sufficiently high to create a transition to classical chaos.