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arXiv:2603.22119 · Physical Review A

Alternative representation of multichannel Rydberg spectra: A modified K -matrix and Lu-Fano plot applied to the manganese spectroscopy

J. Piel, Chris H. Greene

Published May 21, 2026• 0 citations
arXivHTMLPDF

Abstract

The well-known graphical representation called the Lu-Fano plot was originally developed for multi-channel Rydberg spectroscopy, especially in quantum defect theory. The present study shows some of the limitations of this traditional Lu-Fano plot that are desirable to improve on, when there are closely split ionization thresholds as in many current generation quantum information applications involving hyperfine-split thresholds, or when there are more than two ionization threshold energies. The modified representation introduced here is especially simplifying in the situation where one is exploring the bound states lying very far below those closely split thresholds. Moreover, it overcomes one limitation, namely that in contrast to the traditional Lu-Fano plot, the modified representation developed here can be utilized for problems where there more than two ionization thresholds. An example application to Rydberg series of the manganese atom illuminates its use in a practical problem.

DOI
10.1103/2rr5-bzhw

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The well-known graphical representation called the Lu-Fano plot was originally developed for multi-channel Rydberg spectroscopy, especially in quantum defect theory. The present study shows some of the limitations of this traditional Lu-Fano plot that are desirable to improve on, when there are closely split ionization thresholds as in many current generation quantum information applications involving hyperfine-split thresholds, or when there are more than two ionization threshold energies. The modified representation introduced here is especially simplifying in the situation where one is exploring the bound states lying very far below those closely split thresholds. Moreover, it overcomes one limitation, namely that in contrast to the traditional Lu-Fano plot, the modified representation developed here can be utilized for problems where there more than two ionization thresholds. An example application to Rydberg series of the manganese atom illuminates its use in a practical problem.
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Abstract A method for calculating the properties of Rydberg states and Rydberg–Rydberg interaction between two 87 Sr atoms is described. The method is based on a multichannel quantum defect theory description of the Rydberg states that accounts for the hyperfine splitting of the 87 Sr + ground state. Results are given for the scalar and tensor polarizabilities and the eigenvalues of the C 6 matrix for the 5 sns F T = 9/2 series. These results illustrate the new features that arise due to the hyperfine splitting of the thresholds. In particular, there should be several couple Förster resonances above n = 50 unlike the case of 88 Sr which has none.
Quantum information processing with neutral atoms relies on Rydberg excitation for entanglement generation. While the use of heavy divalent or open-shell elements, such as strontium or ytterbium, has benefits due to their optically active core and a variety of possible qubit encodings, their Rydberg structure is generally complex. For some isotopes in particular, hyperfine interactions are relevant even for highly excited electronic states. We employ multichannel quantum defect theory to infer the Rydberg structure of isotopes with nonzero nuclear spin and perform nonperturbative Rydberg-pair interaction calculations. We find that due to the high level density and sensitivities to external fields, experimental parameters must be precisely controlled. Specifically in Sr 87 , we study an intrinsic Förster resonance, unique to divalent atoms with hyperfine-split thresholds, which simultaneously provides line stability with respect to external field fluctuations and enhanced long-range interactions. Additionally, we provide parameters for pair states that can be effectively described by single-channel Rydberg series. The explored pair states provide exciting opportunities for applications in the blockade regime, as well as for more exotic long-range interactions such as largely flat, distance-independent potentials. Published by the American Physical Society 2024
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For many purposes it is desirable to have an easily understandable and accurate picture of the atomic states. This is especially true for the highly excited states which exhibit features not present in the well known states hydrogen-like orbitals with usual values of the quantum numbers. It could be expected that such visualizations are readily available. Unfortunately, that is not the case. We illustrate the problems by showing several less fortunate earlier presentations in some scientifically most valuable works, and show more suitable visualizations for those cases. The selected cases are not chosen to criticize the authors' approach. Rather, we have taken these very important papers to underline the need for serious work with graphical representations which this work attempts to be a part of. In this text we discuss the problems encountered when visualizing Rydberg states, review some existing presentations and propose guidelines for applications. The focus of this work are so called Stark states and coherent elliptic states of Rydberg atoms. In the sections on elliptic states we show some quite novel geometric interpretations which should be very helpful in analysis of Rydberg state manipulations in external fields. Our demonstration examples involve only hydrogen-like states. However, the techniques and analysis are also relevant for Rydberg molecules and more complicated highly excited atomic and molecular systems.
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).