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arXiv:1402.5802 · Journal of Physics B Atomic Molecular and Optical Physics

Multichannel quantum defect theory of strontium bound Rydberg states

Christophe L. Vaillant, M P A Jones, R. M. Potvliege

Published Jul 15, 2014• 40 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0953-4075/47/15/155001

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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.
We present calculations of long-range interactions in Rydberg atoms, with a focus on the dipole-dipole interactions of strontium Rydberg states. The growing use of Rydberg states in the field of cold atoms necessitates a more detailed understanding of the effects of dipole-dipole interactions, which are currently being investigated in a number of research groups worldwide. Calculations of long-range interactions in Rydberg states of caesium, cal- cium, rubidium, strontium and ytterbium are presented. By taking the one active electron approximation we develop consistent models of these long- range interactions, and construct a survey of the Rydberg state dipole-dipole interactions and quadrupole-quadrupole interactions. We compare the inter- actions between series and between atoms, highlighting the importance of certain series for applications suggested in previous works. In order to include two-electron effects in the description of dipole-dipole interactions in divalent atoms, we use multichannel quantum defect theory (MQDT) to develop models of the Rydberg series of strontium. We use an empirical reactance matrix formalism, where the reactance matrix is fitted to reproduce experimentally measured values of the bound state energy levels. Models are found for all series of strontium with L ≤ 3. We extend the MQDT formalism to the description of the natural radiative lifetimes of strontium, where the perturbers are found to have a large quenching effect on these lifetimes. By incorporating the MQDT description of the Rydberg states of strontium into the calculation of dipole-dipole interactions, we find a spin-forbidden two-atom resonance in the 3D2 states of strontium. We consider a one- dimensional lattice of strontium atoms, and find that the internal dynamics of the Rydberg atoms demonstrates spin transport for large lattice spacings and a separation of the spin and total angular momentum dynamics for small lattice spacings. Spin-angular momentum separation (analogous to spin-charge separation in condensed matter) in strontium Rydberg atoms may have uses in the investigation of one-dimensional Fermi gases and their description using Luttinger liquid theory.
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By combining the quantum theory of radiative transition with multichannel quantum-defect theory, we have derived a general formula to calculate the lifetimes of highly excited states for atoms. As an example, we have evaluated the lifetimes for the perturbed 6snd 1D2^{1}D_{2}1D2​ (n=8--40) and 6snd 3D2^{3}D_{2}3D2​ (n=10--26) Rydberg levels, and the perturbers of the ytterbium atom. We have not only obtained results that are in perfect agreement with the recent measurements, but also predicted the lifetimes of 18 other highly excited states. The results indicate that the dramatic variation for lifetimes of Rydberg states in the vicinity of perturbing states is due to the strong channel interaction.
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.
Rydberg atoms provide a powerful platform for exploring strongly interacting quantum systems, both in free space and in structured electromagnetic environments, with growing applications in quantum technology. Accurately modeling their single-atom properties and mutual interactions is essential for interpreting experiments and designing new architectures. We present a unified theoretical framework for Rydberg atoms and their interactions based on multi-channel quantum defect theory (MQDT) and static electromagnetic Green's tensors. MQDT provides a precise description of Rydberg states of divalent atoms such as strontium and ytterbium, while the Green's tensor formalism provides a general and flexible approach for calculating interactions between two Rydberg atoms in arbitrary geometries, including modifications induced by nearby surfaces. We implement this framework in an updated version of the open-source toolkit PairInteraction [Weber et al., J.~Phys.~B~50 (2017)]. The implementation leverages high-performance libraries and achieves speedups of one order of magnitude for pair-potential calculations compared to prior software. We demonstrate the capabilities of the toolkit through example applications to divalent atoms and show excellent agreement with experimental data for an exemplary Stark map of 174^{174}174Yb. The modular software architecture enables the community to extend it further.