Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Localization of classically chaotic diffusion for hydrogen atoms in microwave fields

J. E. Bayfield, Giulio Casati, Italo Guarneri, David W. Sokol

Published Jul 24, 1989• 155 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.63.364

Related papers

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 eBooks•Apr 27, 1995•85 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, 1991•0 citations

Dynamical localization in more than one dimension

Andreas Buchleitner, Dominique Delande

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.

Physical Review Letters•Jan 4, 1993•27 citations

Excited Atoms in Strong Microwaves: Classical Resonances and Localization in Experimental Final-State Distributions

J. E. Bayfield, David W. Sokol

Highly excited hydrogen atoms have been exposed to an intense pulse of microwaves with frequency near the initial classical electron orbit frequency. Measurements were made of the probability distribution for different bound states after the pulse. Structure in such distributions is found to be near classical, and arises from the presence of a classical resonance island in action-angle space. The measured distributions also yield values of electron localization length in action space that are in agreement with quantum localization theory and with numerical values based on quantum mechanics.

Physical Review Letters•Oct 31, 1988•59 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 Electronics•Jul 1, 1988•235 citations

Quantum Suppression of Microwave Ionization of Rydberg Atoms at High Scaled Frequency

H. Maeda, Thomas F. Gallagher

Microwave ionization of Rydberg atoms is well described as the onset of classical chaos when the microwave frequency omega is less than the Kepler frequency 1/n(3). However, when omega>1/n(3), i.e., at high scaled frequency Omega=omegan(3)>1, classical ionization is predicted to be suppressed by quantum interference, an analogue to Anderson localization in a solid. Using 17.55 GHz microwave fields we have observed the ionization of Sr Rydberg atoms in the regime 1</=Omega</=5 . Our measurements demonstrate the quantum suppression of classical diffusive ionization and show the ionization field to be n independent in this regime.

Physical Review Letters•Nov 4, 2004•17 citations
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.
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.
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.
Highly excited hydrogen atoms have been exposed to an intense pulse of microwaves with frequency near the initial classical electron orbit frequency. Measurements were made of the probability distribution for different bound states after the pulse. Structure in such distributions is found to be near classical, and arises from the presence of a classical resonance island in action-angle space. The measured distributions also yield values of electron localization length in action space that are in agreement with quantum localization theory and with numerical values based on quantum mechanics.
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.>
Microwave ionization of Rydberg atoms is well described as the onset of classical chaos when the microwave frequency omega is less than the Kepler frequency 1/n(3). However, when omega>1/n(3), i.e., at high scaled frequency Omega=omegan(3)>1, classical ionization is predicted to be suppressed by quantum interference, an analogue to Anderson localization in a solid. Using 17.55 GHz microwave fields we have observed the ionization of Sr Rydberg atoms in the regime 1</=Omega</=5 . Our measurements demonstrate the quantum suppression of classical diffusive ionization and show the ionization field to be n independent in this regime.