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Physical Review A

Rydberg states in crossed fields: The gyropendulum

A. R. P. Rau

Published Nov 1, 1986• 2 citations
Publisher

Abstract

The spectrum of degenerate Rydberg states of an $n$-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.

DOI
10.1103/physreva.34.4501

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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.
A spectroscopic study of Rydberg states of helium (n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear (n = 30, B ≤ 120 mT and F = 0-78 V cm⁻¹), and (ii) the diamagnetic term is dominant and the Stark effect is linear (n = 45, B = 277 mT and F = 0-8 V cm⁻¹). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m ₗ values and pronounced m ₁-mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.
Abstract A spectroscopic study of Rydberg states of helium ( n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear ( n = 30, B ≤ 120 mT and F = 0–78 V cm −1 ), and (ii) the diamagnetic term is dominant and the Stark effect is linear ( n = 45, B = 277 mT and F = 0–8 V cm −1 ). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin–orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m l values and pronounced m l -mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg–Stark deceleration.
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.
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-