Physical Review Letters

Dynamical localization in more than one dimension

Andreas Buchleitner, Dominique Delande

Published Jan 4, 1993• 27 citations

Abstract

The ionization of hydrogen atoms by a microwave field is numerically studied, for the first time in a realistic picture, using a fully three-dimensional quantum approach with complete inclusion of the continuum. This provides first evidence for the persistence of dynamical localization in higher-dimensional systems. Comparison to the one-dimensional dynamics as well as to experimental results is given.

DOI: 10.1103/physrevlett.70.33

Related papers

Localization of classically chaotic diffusion for hydrogen atoms in microwave fields

J. E. Bayfield, Giulio Casati, Italo Guarneri +1 more

Physical Review LettersJul 24, 1989155 citations

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

Giulio Casati, Boris V. Chirikov, Italo Guarneri +1 more

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.

Physical Review LettersDec 28, 198739 citations

Localization of classically chaotic diffusion for hydrogen atoms in microwave fields

Giulio Casati, Boris V. Chirikov

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.

Cambridge University Press eBooksApr 27, 199585 citations

Realistic three-dimensional computations of microwave-ionization curves of hydrogen Rydberg atoms

Graham N. Rockwell, V. F. Hoffman, Th. Clausen +1 more

We report a realistic computation of experimentally measured microwave ionization curves of hydrogen Rydberg atoms. The experimental field envelope, the duration of the microwave irradiation, the radial droop of the field in the cavity, and the microcanonical distribution of experimental initial states is completely taken into account. We obtain a strong dependence of the ionization probability on the initial magnetic quantum number. Also, a complete 3D three-way comparison between experiment, quantum, and classical theory in the experimentally relevant parameter regime is presented.

Physical Review AJan 16, 20024 citations

Hydrogen atom in monochromatic field: chaos and dynamical photonic localization

Giulio Casati, Italo Guarneri, Dima L. Shepelyansky

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.>

IEEE Journal of Quantum ElectronicsJul 1, 1988235 citations

Chaotic behaviour in quantum dynamics

Giulio Casati, Italo Guarneri

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.

Sep 1, 19910 citations