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Physical Review Letters

Localization of Diffusive Excitation in the Two-Dimensional Hydrogen Atom in a Monochromatic Field

Giulio Casati, Boris V. Chirikov, Italo Guarneri, Dima L. Shepelyansky

Published Dec 28, 1987• 39 citations
Publisher

Abstract

We present new data from numerical simulations of microwave excitation of a two-dimensional hydrogen atom, which show that in a wide parameter range under the one-dimensional delocalization border, the quantum localization phenomenon persists. We theoretically reconsider the problem of two-dimensional localization, by using an appropriately constructed four-dimensional map over an orbital period of the electron, and thus explain the numerical results.

DOI
10.1103/physrevlett.59.2927

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We present new data from numerical simulations of microwave excitation of a two-dimensional hydrogen atom, which show that in a wide parameter range under the one-dimensional delocalization border, the quantum localization phenomenon persists. We theoretically reconsider the problem of two-dimensional localization, by using an appropriately constructed four-dimensional map over an orbital period of the electron, and thus explain the numerical results.
The quantum localization phenomenon that strongly limits any quantum process of diffusive ionization that may be started in systems subjected to a periodic perturbation is discussed. In the case of a highly excited hydrogen atom in a monochromatic field, this phenomenon is theoretically analyzed by reducing the dynamics to appropriate mappings. It is shown that if the field strength is less than a so-called delocalization border, the distribution over unperturbed levels is exponential in the number of absorbed photons and the corresponding localization length is determined. Using the mapping description, it is shown that the excitation process occurring in a two-dimensional atom proceeds essentially along the same lines as in the one-dimensional model. These predictions are supported by results of numerical simulation, and the possibility of their experimental verification is discussed.>
Analytical and numerical results are presented on the mechanism of excitation and ionization of hydrogen atoms under microwave fields. In particular the existence is predicted of a critical value of the microwave field, the quantum delocalization border, above which the quantum packet delocalizes and strong excitation and ionization takes place. Below the quantum border, the packet is localized even though the correseponding classical system is chaotic and obeys a diffusion equation. These studies reveal some other unexpected new features of quantum dynamics which aslo could be observed in laboratory experiments and provides a quantum theory for subthreshold ionization. Keywords: Quantum Chaos; Energy Level Statistics; Quantum Kicked Rotator; Anderson Localization; Microwave Excitation of Hydrogen Atoms; Keldish Parameter; Quantum Diffusion; Italy.
I show that the theory developed for quantum delocalization of an excited hydrogen atom in a two-frequency linearly polarized microwave field can be used with a few adaptions to explain the quantum delocalization of alkali-metal atoms in a linearly polarized monochromatic field in the regime where it deviates from hydrogenic behavior. Comparison with numerical and laboratory experiments is satisfactory: apart from a constant factor, independent from the microwave frequency, the same dependence from the initial quantum number is observed.
New experimental results are presented for short-pulse microwave ionization of highly excited hydrogen atoms. A comparison of these results with quantum numerical computations and analytical predictions provides for the first time experimentally grounded evidence of the localization phenomenon that leads to the suppression of the quantum version of the chaotic diffusion in action space occurring in the classical limit. The onset of chaotic motion in externally driven classical systems is a key problem in nonlinear dynamics that is now well understood in its essential aspects. In many physically interesting cases, as the perturbation strength increases beyond some critical value, the system starts absorbing energy in a diffusive way. The question whether “diffusive” excitation processes can take place also in externally driven quantum systems is then a very interesting one for the physics of atoms and molecules in external electromagnetic fields. This is a deep question involving the nature and the validity of the quasiclassical approximation when the underlying classical dynamics is chaotic. The question of “quantum diffusion” was first addressed in a simple model system, the kicked rotator. It was chosen because the features of classical chaos in it were relatively clean and well understood. Besides that, the numerical simulation of its quantum dynamics could be easily accomplished. The major indication of this model was that quantum mechanics suppresses the classical chaotic diffusion in action via a destructive interference effect similar to that responsible for the Anderson localization well known in condensed matter physics.