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Physical Review A

Autoionization of Rydberg states with large angular momentum: Application to alkaline-earth atoms

Michel Poirier

Published Oct 1, 1988• 51 citations
Publisher

Abstract

This paper is devoted to the autoionization process of large-angular-momentum Rydberg states. After a brief account of autoionization formalism in nonrelativistic theory and single-configuration approximation, we apply it to atomic states with one electron of large angular momentum. The dominant contribution is the direct one and the exchange contribution is ignored. In this framework, the autoionization width varies with the principal quantum number as ${n}^{\mathrm{\ensuremath{-}}3}$ and exponentially with the angular momentum. When two excited electrons interact with a spherically symmetric core, it is demonstrated that the interaction between the Rydberg electron and the core polarized by the valence electron is proportional to the interaction between the two active electrons. Using newly derived radial matrix elements, we obtain a generally good agreement between our results and experiments on barium and strontium. Large-l Rydberg states are shown to be stable versus autoionization as soon as l is about 7. Possible refinements of our method are reviewed.

DOI
10.1103/physreva.38.3484

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This paper is devoted to the autoionization process of large-angular-momentum Rydberg states. After a brief account of autoionization formalism in nonrelativistic theory and single-configuration approximation, we apply it to atomic states with one electron of large angular momentum. The dominant contribution is the direct one and the exchange contribution is ignored. In this framework, the autoionization width varies with the principal quantum number as n\ensuremath−3{n}^{\mathrm{\ensuremath{-}}3}n\ensuremath−3 and exponentially with the angular momentum. When two excited electrons interact with a spherically symmetric core, it is demonstrated that the interaction between the Rydberg electron and the core polarized by the valence electron is proportional to the interaction between the two active electrons. Using newly derived radial matrix elements, we obtain a generally good agreement between our results and experiments on barium and strontium. Large-l Rydberg states are shown to be stable versus autoionization as soon as l is about 7. Possible refinements of our method are reviewed.
Abstract In this brief review, the opportunities that the alkaline-earth elements offer for studying new aspects of Rydberg physics are discussed. For example, the bosonic alkaline-earth isotopes have zero nuclear spin which eliminates many of the complexities present in alkali Rydberg atoms, permitting simpler and more direct comparison between theory and experiment. The presence of two valence electrons allows the production of singlet and triplet Rydberg states that can exhibit a variety of attractive or repulsive interactions. The availability of weak intercombination lines is advantageous for laser cooling and for applications such as Rydberg dressing. Excitation of one electron to a Rydberg state leaves behind an optically active core ion allowing, for high- L states, the optical imaging of Rydberg atoms and their (spatial) manipulation using light scattering. The second valence electron offers the possibility of engineering long-lived doubly excited states such as planetary atoms. Recent advances in both theory and experiment are highlighted together with a number of possible directions for the future.
We study isolated core excitation of ultracold ytterbium Rydberg atoms of high orbital angular momentum quantum number $\ensuremath{\ell}$. Measurements were performed on the $6{s}_{1/2}40\ensuremath{\ell}\ensuremath{\rightarrow}6{p}_{1/2}40\ensuremath{\ell}$ transition with $\ensuremath{\ell}=5--9$. The extracted energy shifts and autoionization rates are in good agreement with a model based on independent electrons, taking interactions into account in a perturbative approach. We reveal a slow decrease in the autoionization rates with $\ensuremath{\ell}$, explained by the strong coupling of the $6{p}_{1/2}n\ensuremath{\ell}$ autoionizing state with the $5{d}_{3/2}\ensuremath{\epsilon}{\ensuremath{\ell}}^{\ensuremath{'}}$ continua compared to previously studied divalent atoms.
The theory is developed for one- and two-atom interactions when the atom has a Rydberg electron attached to a hyperfine-split core state. This situation is relevant for some of the rare-earth and alkaline-earth atoms that have been proposed for experiments on Rydberg-Rydberg interactions. For the rare-earth atoms, the core electrons can have a very substantial total angular momentum JJJ and a nonzero nuclear spin III. In the alkaline-earth atoms there is a single (sss) core electron whose spin can couple to a nonzero nuclear spin for odd isotopes. The resulting hyperfine splitting of the core state can lead to substantial mixing between the Rydberg series attached to different thresholds. Compared to the unperturbed Rydberg series of the alkali-metal atoms, the series perturbations and near degeneracies from the different parity states could lead to qualitatively different behavior for single-atom Rydberg properties (polarizability, Zeeman mixing and splitting, etc.) as well as Rydberg-Rydberg interactions (C5{C}_{5}C5​ and C6{C}_{6}C6​ matrices).
Cold gases of Rydberg atoms are an ideal system in which to study the novel effects of strong interatomic interactions. This thesis describes the design and construction of the world's first experiment to study Rydberg states in a cold gas of an alkaline earth metal, in this particular case strontium. We have studied a wide range of Rydberg states, and have developed a sensitive ``step-scan" spectroscopic technique that detects the spontaneous ionization of the Rydberg gas. The step-scan method is used to acquire Stark maps, and these measurements verify a single-electron model for calculating dipole matrix-elements. From the matrix-elements, interaction strengths between strontium Rydberg atoms have been calculated for the first time. The presence of two valence electrons in an alkaline earth metal, such as strontium, offers a new angle on the study of Rydberg atoms. We create doubly excited ``autoionizing" states, the first such study in a cold gas. Autoionization is used as a high yield probe of Rydberg states, and enables a study of excitation dynamics with nanosecond time-resolution. We show that autoionization can quantitatively identify and elucidate state mixing in the Rydberg gas, and probe population transfer at the very onset of ultra-cold plasma formation.
We discuss the systematics of energy levels of high-angular-momentum Rydberg states of alkali-metal atoms, and show that they are well described by a quantum-defect model. Polarization of the core electrons by the valence electron is shown to be the dominant contribution to the quantum defect. As an example, recently observed splittings between the l=3,4,and5l=3,4,\mathrm{and} 5l=3,4,and5 levels in various Rydberg states of sodium are analyzed to yield values for the core polarizabilities. Effective values of the dipole and quadrupole polarizability of 1.0015(15) and 0.48(15) a.u., respectively, are obtained. Implications for the precise determination of the structure of highly excited Rydberg states in alkali atoms are discussed.
The present review is devoted to the recent advances performed in alkaline-earth atoms by the selective laser preparation of autoionizing asymmetrical double Rydberg states which have, so far, not been observed in natural environments. Because the great amount of flexibility achieved by the sequential laser electron excitations, a wide choice of two-electron situations have been investigated and analyzed which exhibit spectral features due to long-range effects of the Coulomb electron-electron repulsion. To overcome the autoionization broadening of the lines, double Rydberg states with a non-core penetrating high-ℓ outer electron were produced by combining temporal laser excitation technique with the electric-field switching method. The study of the spectral correlation signatures in Nsn ℓ double Rydberg states versus ℓ allow to understand their evolution from simple spectra (ℓ ⩾ 10) due to long-range dipole interaction to more complex data (ℓ ⩽ 7) induced by short-range multipole effects when two electrons start to influence more each other.