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arXiv:cond-mat/9911200 · Physical Review Letters

Quantum Poincaré Recurrences for a Hydrogen Atom in a Microwave Field

Giuliano Benenti, Giulio Casati, Giulio Maspero, Dima L. Shepelyansky

Published May 1, 2000• 19 citations
arXivHTMLPDF

Abstract

We study the time dependence of the ionization probability of Rydberg atoms driven by a microwave field, both in classical and in quantum mechanics. The quantum survival probability follows the classical one up to the Heisenberg time and then decays algebraically as P(t) approximately 1/t. This decay law derives from the exponentially long times required to escape from some region of the phase space, due to tunneling and localization effects. We also provide parameter values which should allow one to observe such decay in laboratory experiments.

DOI
10.1103/physrevlett.84.4088

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We investigate the ionization of a 1-D quantum system with a zero-range attractive potential at x = 0 when it is subjected to a time dependent harmonic zero range potential forcing of frequency /spl omega/, strength r, at position x = a. We show that the ionization probability goes to 1 as time t /spl rarr/ /spl infin/ for almost all values of r, /spl omega/, and a. The initially exponential decay of the probability to stay in the bound state is followed at later time by a t/sup -3/ law if r is small and /spl omega/ is not close to resonances. When this is not true the separation between the exponential and power law decay regimes disappears and Fermi's golden rule fails. There exist exceptional sets of parameters where the survival probability never decays to zero and complete ionization is impossible.