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Physical Review A

Rydberg-atom wave packets localized in the angular variables

John A. Yeazell, Carlos R. Stroud

Published Apr 1, 1987• 57 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.35.2806

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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 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.
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 present a theoretical construction for closest-to-classical wave packets localized in both angular and radial coordinates and moving on a keplerian orbit. The method produces a family of elliptical squeezed states for the planar Coulomb problem that minimize appropriate uncertainty relations in radial and angular coordinates. The time evolution of these states is studied for orbits with different semimajor axes and eccentricities. The elliptical squeezed states may be useful for a description of the motion of Rydberg wave packets excited by short-pulsed lasers in the presence of external fields, which experiments are attempting to produce. We outline an extension of the method to include certain effects of quantum defects appearing in the alkali-metal atoms used in experiments.
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 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.