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Physical Review A

Asymmetric-top description of Rydberg-electron dynamics in crossed external fields

M. J. Gourlay, T. Uzer, David Farrelly

Published Apr 1, 1993• 41 citations
Publisher

Abstract

Rydberg atoms in external electric and magnetic fields have recently emerged as atomic-scale laboratories where the quantum mechanics of classically nonintegrable systems can be studied. In this article we show, using classical canonical perturbation theory, how the intricate nonlinear dynamics of a Rydberg electron in crossed electric and magnetic fields can be described in terms of two coupled asymmetric tops.

DOI
10.1103/physreva.47.3113

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Rydberg atoms in external electric and magnetic fields have recently emerged as atomic-scale laboratories where the quantum mechanics of classically nonintegrable systems can be studied. In this article we show, using classical canonical perturbation theory, how the intricate nonlinear dynamics of a Rydberg electron in crossed electric and magnetic fields can be described in terms of two coupled asymmetric tops.
The spectrum of a Rydberg atom in crossed electric and magnetic fields has been calculated by the methods of classical perturbation theory. Much consideration is given to the region of almost degenerate frequencies, involving mutually normal orientations of fields of any relative value, and also the case when one of the fields is very weak. Strong anisotropy of the electric polarisability in a magnetic field is predicted. In particular, longitudinal and transverse polarisabilities have different signs. The magnetic polarisability in an electric field has been found.
The spectrum of degenerate Rydberg states of an nnn-manifold of the hydrogen atom when placed in crossed (perpendicular) electric and magnetic fields (the diamagnetic term is disregarded) is shown to conicide with that of a charged-particle harmonic oscillator in a magnetic field. A mechanical counterpart is identified as the gyropendulum. These correspondences give further insight into the nature of Rydberg states in external fields.
Due to its academic significance and potential applications, the study of the behavior of Rydberg atoms in external fields has been a topic in the forefront of atomic and molecular physics researches. Efforts are currently concentrated on the situations with the presence of both the electric and the magnetic fields (combined fields). In particular, when the two fields are perpendicular to each other, the potential symmetry is severely destructed and the system becomes very complicated. Previous theoretical studies predicted the exist-