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Journal of Physics B Atomic and Molecular Physics

Effect of crossed electric and magnetic fields on sodium Rydberg states

Eric J. Korevaar, Michael G. Littman

Published Aug 14, 1983• 79 citations
Publisher

Abstract

The excitation spectrum for Rydberg states near n=11 of atomic sodium in crossed electric and magnetic fields has been recorded. The theoretical analysis of the spectroscopic data reveals degeneracies among some sublevels even though different sublevels are mixed by the external fields. The degeneracies are traced to a dynamical symmetry that is characteristic of the Coulomb potential.

DOI
10.1088/0022-3700/16/15/003

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The excitation spectrum for Rydberg states near n=11 of atomic sodium in crossed electric and magnetic fields has been recorded. The theoretical analysis of the spectroscopic data reveals degeneracies among some sublevels even though different sublevels are mixed by the external fields. The degeneracies are traced to a dynamical symmetry that is characteristic of the Coulomb potential.
The excitation spectrum of atomic sodium in crossed electric and magnetic fields has been recorded. Data for states near n = 11 are found to be in good agreement with theoretical estimates of line positions. The agreement with estimates of line strengths, however, is only fair. The lack of complete agreement between simple hydrogenic theory and experiment can be traced t o a breakdown of the assumption that the influence of the nearby 12p state is negligibly small. The significance of this experiment is that, for the first time, clear evidence of m-mixing between bound states has been obtained. The dominant effect of the m-mixing has been to make accessible optically many Rydberg states. These states in the presence of electric or magnetic fields alone would not have been accessible because of selection rules on m.
The results of an experimental study of the Rydberg spectrum of rubidium in crossed electric and magnetic fields are reported and compared with theoretical predictions. The present investigations have been conducted in the low-field regime in which the paramagnetic and linear Stark interactions are perturbations to the Coulomb energy. When quantum-defect corrections are negligible, the SO(4) symmetry of the Coulomb interaction organizes the hydrogenic energy spectrum according to the law En{\mathit{E}}_{\mathit{n}}En​,k=-R/n2{\mathit{n}}^{2}n2+\ensuremath{\Elzxh}k(${\mathrm{\ensuremath{\omega}}}_{\mathit{L}}^{2}$+${\mathrm{\ensuremath{\omega}}}_{\mathit{S}}^{2}$)1/2{)}^{1/2})1/2, where k is an integer such that -(n-1)\ensuremath{\le}k\ensuremath{\le}(n-1), and ${\mathrm{\ensuremath{\omega}}}_{\mathit{L}}$,${\mathrm{\ensuremath{\omega}}}_{\mathit{S}}$, are, respectively, the Larmor and linear Stark frequencies. The experimental evidence for such a quantization is presented in rubidium Rydberg series using Doppler-free two-photon spectroscopy. The role of quantum defects is incorporated into the theory and experimentally demonstrated.
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.
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-
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.