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

Journal of Experimental and Theoretical Physics

Forms of localization of Rydberg wave packets

E. A. Shapiro

Published Sep 1, 2000• 12 citations
Publisher

Abstract

A graphic method for describing the localization of quantum wave packets in several dimensions is proposed. The method employs classical action-angle coordinates. Different kind of wave packets arising in the two-and three-dimensional Coulomb problems are described from a unified point of view. Specifically, a more precise interpretation of the structure of “angular” Rydberg wave packets is given. Certain additional features of the proposed approach are discussed.

DOI
10.1134/1.1320077

Related papers

Spatially localized Rydberg atom wave packets

John A. Yeazell, Carlos R. Stroud

The quantum theory of atoms is based on a Hamiltonian which is just that of the classical Kepler theory of planetary orbits. In spite of this common foundation, the predictions of the quantum theory ordinarily do not much resemble those of the classical theory. Even in the limit of large quantum numbers the energy eigenstates of quantum theory do not look at all like the classical elliptical orbits. Recently, Parker and Stroud1 showed that it is possible to excite a Rydberg atomic wave packet localized in the radial coordinate. Also, Yeazell and Stroud2 showed that a wave packet localized in the angular coordinates can be formed. Both wave packets exhibit an evolution describable, at least in part, by classical theory. However, neither wave packet truly corresponds to a wave packet traveling in a classical elliptical orbit. We discuss the manner in which such a wave packet might be formed using a short-pulsed laser and arf dressing field. The evolution of the resulting wave packet is compared with that of its classical counterpart.

Annual Meeting Optical Society of America•Jan 1, 1987•0 citations

Keplerian squeezed states and Rydberg wave packets

Robert Bluhm, V. Alan Kostelecký, Bogdan Tudose

We construct minimum-uncertainty solutions of the three-dimensional Schr\"odinger equation with a Coulomb potential. These wave packets are localized in radial and angular coordinates and are squeezed states in three dimensions. They move on elliptical Keplerian trajectories and are appropriate for the description of the corresponding Rydberg wave packets, the production of which is the focus of current experimental effort. We extend our analysis to incorporate the effects of quantum defects in alkali-metal atoms, which are used in experiments. \textcopyright{} 1996 The American Physical Society.

arXiv:quant-ph/9510023•Physical Review A•Feb 1, 1996•21 citations

Rydberg atom wave packets localized in the angular coordinates

John A. Yeazell, Carlos R. Stroud

The quantum theory of atoms is based on a Hamiltonian which is just that of the classical Kepler theory of planetary orbits. In spite of this common foundation, the predictions of quantum theory ordinarily do not much resemble those of classical theory. Even in the limit of large quantum numbers the energy eigenstates of quantum theory do not look at all like the classical elliptical orbits. Recently, Parker and Stroud1 have shown that it is possible to excite a Rydberg atom wave packet whose radial dependence resembles the classical ideal of a particle traveling in an elliptical orbit. In this paper we discuss the formation of a wave packet in the polar and azimuthal angles by the coherent excitation of Rydberg states with the same principal quantum, but with a distribution of the angular momentum quantum numbers. When this wave packet is formed of the Rydberg states of an alkali atom the connection with classical theory is again striking. The wave packet precesses due to the core polarization, just as the classical elliptical orbit precesses due to an added r–4 perturbing potential.

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations

Rydberg wave packets on elliptical orbits

E. A. Shapiro, Paolo Bellomo

We predict and confirm numerically the existence of localized Rydberg wave packets that travel on classical elliptical trajectories with negligible spreading. These wave packets are supported by a resonant circularly polarized microwave field, and we study them by a semiclassical action-angle representation.

Physical Review A•Aug 1, 1999•5 citations

Rydberg-atom wave packets localized in the angular variables

John A. Yeazell, Carlos R. Stroud

Calculations are presented that show the behavior of a wave packet composed of alkali-metal-atom Rydberg states. We demonstrate that it is possible to localize such a wave packet in the polar and azimuthal angles. The evolution of this wave packet is equivalent to the precession of a classical Kepler orbit under the influence of a perturbing potential. In this case, the perturbation is the quantum defect of the alkali-metal atoms. An excitation scheme is proposed for producing these states and the results of a numerical model based on this scheme are presented. Finally, the interaction of these angularly localized wave packets with external fields is discussed and a method of detection is suggested.

Physical Review A•Apr 1, 1987•57 citations

Investigation of Localized Wave Packets of Rydberg Atoms

Natalia I. Teper, Vladimir Leonardovich Derbov

The results of numerical simulation of the Rydberg states laser excitation for the purpose of the forming of localized wave packets, are provided. The action of linear and circularly polarized fields upon an atom is considered for different time dependencies of the pulse envelope. The form and the properties of the obtained packet, constructed from eigen states with low orbital and magnetic quantum numbers have been analyzed. The obtained results are in agreement with the results provided by other authors.

Telecommunications and Radio Engineering•Jan 1, 2009•0 citations
A graphic method for describing the localization of quantum wave packets in several dimensions is proposed. The method employs classical action-angle coordinates. Different kind of wave packets arising in the two-and three-dimensional Coulomb problems are described from a unified point of view. Specifically, a more precise interpretation of the structure of “angular” Rydberg wave packets is given. Certain additional features of the proposed approach are discussed.
The quantum theory of atoms is based on a Hamiltonian which is just that of the classical Kepler theory of planetary orbits. In spite of this common foundation, the predictions of the quantum theory ordinarily do not much resemble those of the classical theory. Even in the limit of large quantum numbers the energy eigenstates of quantum theory do not look at all like the classical elliptical orbits. Recently, Parker and Stroud1 showed that it is possible to excite a Rydberg atomic wave packet localized in the radial coordinate. Also, Yeazell and Stroud2 showed that a wave packet localized in the angular coordinates can be formed. Both wave packets exhibit an evolution describable, at least in part, by classical theory. However, neither wave packet truly corresponds to a wave packet traveling in a classical elliptical orbit. We discuss the manner in which such a wave packet might be formed using a short-pulsed laser and arf dressing field. The evolution of the resulting wave packet is compared with that of its classical counterpart.
We construct minimum-uncertainty solutions of the three-dimensional Schr\"odinger equation with a Coulomb potential. These wave packets are localized in radial and angular coordinates and are squeezed states in three dimensions. They move on elliptical Keplerian trajectories and are appropriate for the description of the corresponding Rydberg wave packets, the production of which is the focus of current experimental effort. We extend our analysis to incorporate the effects of quantum defects in alkali-metal atoms, which are used in experiments. \textcopyright{} 1996 The American Physical Society.
The quantum theory of atoms is based on a Hamiltonian which is just that of the classical Kepler theory of planetary orbits. In spite of this common foundation, the predictions of quantum theory ordinarily do not much resemble those of classical theory. Even in the limit of large quantum numbers the energy eigenstates of quantum theory do not look at all like the classical elliptical orbits. Recently, Parker and Stroud1 have shown that it is possible to excite a Rydberg atom wave packet whose radial dependence resembles the classical ideal of a particle traveling in an elliptical orbit. In this paper we discuss the formation of a wave packet in the polar and azimuthal angles by the coherent excitation of Rydberg states with the same principal quantum, but with a distribution of the angular momentum quantum numbers. When this wave packet is formed of the Rydberg states of an alkali atom the connection with classical theory is again striking. The wave packet precesses due to the core polarization, just as the classical elliptical orbit precesses due to an added r–4 perturbing potential.
Calculations are presented that show the behavior of a wave packet composed of alkali-metal-atom Rydberg states. We demonstrate that it is possible to localize such a wave packet in the polar and azimuthal angles. The evolution of this wave packet is equivalent to the precession of a classical Kepler orbit under the influence of a perturbing potential. In this case, the perturbation is the quantum defect of the alkali-metal atoms. An excitation scheme is proposed for producing these states and the results of a numerical model based on this scheme are presented. Finally, the interaction of these angularly localized wave packets with external fields is discussed and a method of detection is suggested.
The results of numerical simulation of the Rydberg states laser excitation for the purpose of the forming of localized wave packets, are provided. The action of linear and circularly polarized fields upon an atom is considered for different time dependencies of the pulse envelope. The form and the properties of the obtained packet, constructed from eigen states with low orbital and magnetic quantum numbers have been analyzed. The obtained results are in agreement with the results provided by other authors.