Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1711.10518 · Physical Review A

Theory of long-range interactions for Rydberg states attached to hyperfine-split cores

F. Robicheaux, Donald W. Booth, Mark E. Saffman

Published Feb 15, 2018• 25 citations
arXivHTMLPDF

Abstract

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 $J$ and a nonzero nuclear spin $I$. In the alkaline-earth atoms there is a single ($s$) 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 (${C}_{5}$ and ${C}_{6}$ matrices).

DOI
10.1103/physreva.97.022508

Related papers

Engineering Rydberg-pair interactions in divalent atoms with hyperfine-split ionization thresholds

Frederic Hummel, Sebastian Weber, Johannes Mögerle +5 more

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

arXiv:2408.00195•Physical Review A•Oct 18, 2024•7 citations

Recent advances in Rydberg physics using alkaline-earth atoms

F. B. Dunning, T. C. Killian, S. Yoshida +1 more

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.

Journal of Physics B Atomic Molecular and Optical Physics•May 9, 2016•49 citations

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

Michel Poirier

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.

Physical Review A•Oct 1, 1988•51 citations

Long-range interactions between the alkali-metal atoms and alkaline earth ions

Jasmeet Kaur, D. K. Nandy, Bindiya Arora +1 more

Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca$^+$, Ba$^+$, Sr$^+$, and Ra$^+$ alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation $R$. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus $R$ are given among all the considered atoms and ions.

arXiv:1409.7154•Sep 25, 2014•0 citations

Long-range interactions in one- and two-electron Rydberg atoms

Christophe L. Vaillant

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.

•Jan 1, 2014•4 citations

Polarizability of Rydberg atoms and the dominant long-range interactions

Yukap Hahn

The dominant long-range interaction of an alkali-metal atom with charged particles at low energies is given for large separation R by the dispersive potential $W\ensuremath{\simeq}\ensuremath{-}{\ensuremath{\alpha}}_{d}{/R}^{4}$ in terms of the dipole polarizability ${\ensuremath{\alpha}}_{d}.$ For atoms prepared initially in Rydberg states of quantum numbers (n, l), the potential assumes a more complicated form due to the complete or near degeneracy of the n manifold. Contributions to the polarizability are treated in two parts, (a) one for the nondegenerate states and (b) the other for the degenerate or near degenerate cases. It is shown that ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\alpha}}}_{d}^{(b)}$ for case (b) is in general R dependent, and in the limit of complete degeneracy, diverges as ${R}^{2}.$ That is, for a small energy gap \ensuremath{\Delta} between a pair of nearly degenerate states which are dipole coupled, the dispersion potential ${W}^{(b)}\ensuremath{\simeq}{D/R}^{2}$ for $R<{R}_{x}$ and ${W}^{(b)}\ensuremath{\simeq}\ensuremath{-}{\ensuremath{\alpha}}_{d}^{(b)}{/R}^{4}$ for $R>{R}_{x},$ where D is the dipole moment, ${R}_{x}=[2|D/\ensuremath{\Delta}|{]}^{1/2},$ and ${\ensuremath{\alpha}}_{d}^{(b)}\ensuremath{\simeq}{D}^{2}/\ensuremath{\Delta}.$ They may also compete with a ${1/R}^{3}$ potential for Rydberg atoms with $l>0.$ The total ${\ensuremath{\alpha}}_{d}$ can be very large in magnitude for small \ensuremath{\Delta} and even assume negative values, but the corresponding ${R}_{x}$ also increases as \ensuremath{\Delta} decreases. The validity region in R of the ${R}^{\ensuremath{-}4}$ behavior of the potential recedes to larger R as the polarizability grows. A general formula for ${\ensuremath{\alpha}}_{d}$ is given, taking into account the effects of fine-structure splitting, the Lamb shift, and quantum defects.

Physical Review A•Sep 11, 2000•7 citations
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).
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
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.
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.
Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca+^++, Ba+^++, Sr+^++, and Ra+^++ alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation RRR. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus RRR are given among all the considered atoms and ions.
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.
The dominant long-range interaction of an alkali-metal atom with charged particles at low energies is given for large separation R by the dispersive potential $W\ensuremath{\simeq}\ensuremath{-}{\ensuremath{\alpha}}_{d}{/R}^{4}$ in terms of the dipole polarizability ${\ensuremath{\alpha}}_{d}.$ For atoms prepared initially in Rydberg states of quantum numbers (n, l), the potential assumes a more complicated form due to the complete or near degeneracy of the n manifold. Contributions to the polarizability are treated in two parts, (a) one for the nondegenerate states and (b) the other for the degenerate or near degenerate cases. It is shown that ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\alpha}}}_{d}^{(b)}$ for case (b) is in general R dependent, and in the limit of complete degeneracy, diverges as R2.{R}^{2}.R2. That is, for a small energy gap \ensuremath{\Delta} between a pair of nearly degenerate states which are dipole coupled, the dispersion potential ${W}^{(b)}\ensuremath{\simeq}{D/R}^{2}$ for R<RxR<{R}_{x}R<Rx​ and ${W}^{(b)}\ensuremath{\simeq}\ensuremath{-}{\ensuremath{\alpha}}_{d}^{(b)}{/R}^{4}$ for R>Rx,R>{R}_{x},R>Rx​, where D is the dipole moment, ${R}_{x}=[2|D/\ensuremath{\Delta}|{]}^{1/2},$ and ${\ensuremath{\alpha}}_{d}^{(b)}\ensuremath{\simeq}{D}^{2}/\ensuremath{\Delta}.$ They may also compete with a 1/R3{1/R}^{3}1/R3 potential for Rydberg atoms with l>0.l>0.l>0. The total ${\ensuremath{\alpha}}_{d}$ can be very large in magnitude for small \ensuremath{\Delta} and even assume negative values, but the corresponding Rx{R}_{x}Rx​ also increases as \ensuremath{\Delta} decreases. The validity region in R of the ${R}^{\ensuremath{-}4}$ behavior of the potential recedes to larger R as the polarizability grows. A general formula for ${\ensuremath{\alpha}}_{d}$ is given, taking into account the effects of fine-structure splitting, the Lamb shift, and quantum defects.