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Physical Review A

Microwave spectroscopy of low- l singlet strontium Rydberg states at intermediate n, 50≲n≲70

R. Brienza, Y. Lu, C. Wang, S. K. Kanungo, T. C. Killian, F. B. Dunning, Joachim Burgdörfer, S. Yoshida

Published Aug 28, 2023• 2 citations
Publisher

Abstract

The authors use microwave spectroscopy to measure the quantum defects for lower-$l$ singlet strontium Rydberg states at intermediate $n$. The results are used to develop a revised set of Rydberg-Ritz quantum defect parameters that could help make accurate predictions of the energy intervals between other high-lying states.

DOI
10.1103/physreva.108.022815

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Addendum: Multichannel quantum defect theory of strontium bound Rydberg states (2014 J. Phys. B: At. Mol. Opt. Phys. 47 155001)

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arXiv:2403.08742•Journal of Physics B Atomic Molecular and Optical Physics•Sep 11, 2024•2 citations
The authors use microwave spectroscopy to measure the quantum defects for lower-lll singlet strontium Rydberg states at intermediate nnn. The results are used to develop a revised set of Rydberg-Ritz quantum defect parameters that could help make accurate predictions of the energy intervals between other high-lying states.
Rydberg atoms have a long history of scientific research, but they have recently seen a resurgence in popularity due to their advantages when dealing with coupled internal Rydberg states, or externally-coupled Rydberg atoms. The use of convenient RF and/or microwave generation techniques allows for straightforward coupling of many nearby Rydberg states, enabling quantum simulation studies, such as the generation of a synthetic lattice. Strontium is particularly attractive for Rydberg atom studies due to its optically active core, which allows for two-electron excited states and its conveniently accessible transition frequencies that match those available using commercial diode lasers. Before these experiments and applications can be realized however, precise knowledge of Rydberg state energies and quantum defects is required. Therefore, this work undertakes an extensive study of the quantum defects of both singly and doubly-excited strontium Rydberg atoms for a wide range of n and l. Precision microwave spectroscopy between nearby Rydberg states produces an improved self-consistent set of quantum defects for singly-excited 1S0, 1P1, 1D2, and 1F3 states, described by their corresponding Rydberg-Ritz parameters. Quantum defects and lifetimes for autoionizing two-electron-states are also presented. These elucidate the effects of core penetration by the “outer” excited Rydberg electron on transitions within the core ion and on the Rydberg level itself.
Studies of high-$n, 120\ensuremath{\lesssim}n\ensuremath{\lesssim}160$, strontium 5sng,5snh5sng, 5snh5sng,5snh, and 5sni5sni5sni Rydberg states are reported. Measurements using microwave spectroscopy provide the quantum defects for these states and furnish a valuable test of quantum defects reported for lower-$\ensuremath{\ell}$ states in the high-nnn limit. With increasing $\ensuremath{\ell}$ the relativistic spin-orbit interaction becomes comparable to the electron-electron interaction resulting in the breakdown of the standard LSLSLS-coupling scheme. Heavier alkaline-earth quasi-two-electron systems differ significantly from a true two-electron system such as helium because indirect spin-orbit effects are dramatically enhanced. We explore the high-nnn limit of this transition between LSLSLS and jjjjjj coupling. For high-$\ensuremath{\ell}$ states the quantum defects are determined predominantly by the polarizability of the inner electrons.
We report on the atom loss spectroscopy of strontium Rydberg atoms in a magnetooptical trap, using a two-photon excitation scheme through the intermediate state 5s5p3P15s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}5s5p3P1​. Energies of the 5sns3S15sns{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}5sns3S1​ and 5snd3D1,25snd{\phantom{\rule{0.16em}{0ex}}}^{3}{D}_{1,2}5snd3D1,2​ Rydberg series of 88Sr^{88}\mathrm{Sr}88Sr in the range $13\ensuremath{\le}n\ensuremath{\le}50$ are determined with an absolute accuracy of 10 MHz, including the perturbed region where the 5snd3D25snd{\phantom{\rule{0.16em}{0ex}}}^{3}{D}_{2}5snd3D2​ series couples to the 5snd1D25snd{\phantom{\rule{0.16em}{0ex}}}^{1}{D}_{2}5snd1D2​ series. This represents an improvement by more than two orders of magnitude compared to previously published data. The quantum defects for each series are determined using the extended Rydberg-Ritz formula in the range where there is no strong perturbation. A value of 1377012721(10)MHz1\phantom{\rule{0.16em}{0ex}}377\phantom{\rule{0.16em}{0ex}}012\phantom{\rule{0.16em}{0ex}}721(10)\phantom{\rule{0.28em}{0ex}}\text{MHz}1377012721(10)MHz for the first ionization limit of 88Sr^{88}\mathrm{Sr}88Sr is extracted.
Abstract Using the reactance matrix approach, we systematically develop new multichannel quantum defect theory (MQDT) models for the singlet and triplet S, P, D and F states of strontium below the first ionization limit, based on improved energy level measurements. The new models reveal additional insights into the character of doubly excited perturber states, and the improved energy level measurements for certain series allow fine structure to be resolved for those series’ perturbers. Comparison between the predictions of the new models and those of previous empirical and ab initio studies reveals good agreement with most series; however, some discrepancies are highlighted. Using the MQDT wave functions derived from our models we calculate other observables such as Landé -factors and radiative lifetimes. The analysis reveals the impact of perturbers on the Rydberg state properties of divalent atoms, highlighting the importance of including two-electron effects in the calculations of these properties. The work enables future investigations of properties such as Stark maps and long-range interactions of Rydberg states of strontium.
The use of autoionization as a tool to quantitatively analyze transitions between high-n strontium Rydberg states with low-to-intermediate values of L is described and is demonstrated through observations of Rabi oscillations when driving 5snf 1F3 → 5s(n + 1)g 1G4, 5snf 1F3 → 5s(n + 2)h 1H5, and 5snp 1P1 → 5s(n + 1)d 1D2 transitions using microwave fields. The technique is shown to offer advantages when compared to selective field ionization and can be used with other alkaline-earth and alkaline-earth-like metals.