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arxiv: 2605.14993 · v1 · submitted 2026-05-14 · ⚛️ physics.atom-ph · quant-ph

Recognition: 2 theorem links

· Lean Theorem

Accurate Modeling of Rydberg Atoms and Their Interactions: Theory and Implementation in PairInteraction

Johannes M\"ogerle , Frederic Hummel , Alicia Keil , Tangi Legrand , Eduard J. Braun , Henri Menke , Jonathan King , Beatriz Olmos
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Sebastian Hofferberth Hans Peter B\"uchler Sebastian Weber
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Pith reviewed 2026-05-15 02:48 UTC · model grok-4.3

classification ⚛️ physics.atom-ph quant-ph
keywords Rydberg atomsquantum defect theoryGreen's tensorsatomic interactionsdivalent atomsStark effectquantum technologiespair potentials
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The pith

A framework based on multi-channel quantum defect theory and Green's tensors accurately models Rydberg atoms of divalent species and their interactions in arbitrary geometries.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a unified approach to modeling Rydberg atoms and the forces between them. It uses multi-channel quantum defect theory to handle the complex electron structure of divalent atoms such as strontium and ytterbium. The static electromagnetic Green's tensor method then calculates how these atoms interact when placed in free space or near surfaces. The whole system is coded into an updated PairInteraction program that runs pair-potential calculations ten times quicker than earlier versions. Tests show close matches to measured Stark maps for ytterbium, supporting use in quantum technology designs.

Core claim

The framework provides a precise description of Rydberg states of divalent atoms and a general approach for calculating interactions in arbitrary geometries, with the implementation achieving speedups of one order of magnitude and excellent agreement with experimental data for an exemplary Stark map of 174Yb.

What carries the argument

Multi-channel quantum defect theory combined with static electromagnetic Green's tensors, implemented in the PairInteraction software.

Load-bearing premise

The multi-channel quantum defect theory parameters together with the static Green's tensors are assumed to capture all relevant physics without extra corrections for dynamic or higher-order effects.

What would settle it

An experimental measurement of a Rydberg pair potential or Stark shift near a surface that differs markedly from the Green's tensor prediction would show the model is incomplete.

Figures

Figures reproduced from arXiv: 2605.14993 by Alicia Keil, Beatriz Olmos, Eduard J. Braun, Frederic Hummel, Hans Peter B\"uchler, Henri Menke, Johannes M\"ogerle, Jonathan King, Sebastian Hofferberth, Sebastian Weber, Tangi Legrand.

Figure 1
Figure 1. Figure 1: Considered system. (a) Two interacting Rydberg atoms, either in free space or in a structured electromagnetic environment (the figure depicts a cavity). The atoms can be alkali atoms or divalent atoms. Static electric and magnetic fields can be applied in arbitrary directions. (b) Overview of the approach used to construct the system’s Hamiltonian, starting with the formalisms applied to describe the physi… view at source ↗
Figure 2
Figure 2. Figure 2: MQDT concepts. (a) The calculation of Rydberg energies and channel coefficients with MQDT typically as￾sumes that, beyond a radius rc, the potential of the ionic core is a pure Coulomb potential. As an approximation, Coulomb wave functions can remain useful at shorter distances up to a core region where irregular Coulomb functions diverge, and multi-electron effects dominate. (b) Schematic sketch of the FJ… view at source ↗
Figure 3
Figure 3. Figure 3: Labeling the angular character of the S1/2 Rydberg series of 171Yb. (a) Sketch of the FJ-coupling scheme (left) and LS-coupling scheme (right). For the consid￾ered series, Jtot and Fc are non-trivial quantum numbers. (b) Average value of these quantum numbers (dotted) and their standard deviation (shaded region). As a function of the refer￾ence effective principal quantum number νref, the nearly “good” qua… view at source ↗
Figure 4
Figure 4. Figure 4: Schematic overview of the software archi￾tecture. We separate the calculation of states and matrix elements from the generation and analysis of Hamiltonians for one and two Rydberg atoms. The former is performed by the RydState Python package. The latter is implemented in the PairInteraction Python package, which defines the classes BasisAtom/BasisPair and SystemAtom/SystemPair to repre￾sent the objects re… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the computational perfor￾mance of PairInteraction v2 with v0.9 (on an AMD Ryzen 7 5700G with 62 GiB of RAM). A system of two in￾teracting rubidium atoms is considered, with and without electric and magnetic fields of strength Ez = 0.2 V/cm and Bz = 100 G. We measure the wall-clock time for (a) construct￾ing a two-atom Hamiltonian and (b) computing interaction potentials for 100 interatomic di… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of a measured and calculated Stark map in 174Yb. The Stark map shows an avoided crossing of the ∣49.7S0, Stot = 0.00, m = 0⟩ with the nearby ∣49.7F3, Stot = 0.00, m = 0⟩ state. The green colormap shows the ion counts in the experiment for the given electric field and two-photon detuning, plotted as energy on the y-axis. The gray lines are the calculated energy levels, and the colored markers add… view at source ↗
Figure 8
Figure 8. Figure 8: Rydberg interactions near a perfectly con￾ducting plate. (a) The self-interaction of a single Rydberg atom near a plate at distance d. (b) The C6 coefficient of the pair state ∣69S1/2, m = 1/2; 72S1/2, m = 1/2⟩ of two rubidium atoms as a function of the distance d to the plate. For com￾parison, we performed the calculation with (blue solid line) and without (orange dashed line) including the self-interacti… view at source ↗
read the original abstract

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 PairInteraction software [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 framework through example applications to divalent atoms and show excellent agreement with experimental data for an exemplary Stark map of $^{174}$Yb. The modular software architecture enables the community to extend it further.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a unified theoretical framework combining multi-channel quantum defect theory (MQDT) for precise description of Rydberg states in divalent atoms such as strontium and ytterbium with the static electromagnetic Green's tensor formalism for calculating pairwise interactions in arbitrary geometries, including surface modifications. This is implemented in an updated open-source PairInteraction software package that leverages high-performance libraries to achieve speedups of one order of magnitude for pair-potential calculations. Capabilities are demonstrated through example applications to divalent atoms, with excellent agreement shown against experimental data for the Stark map of ^{174}Yb.

Significance. If the framework's approximations hold, the work provides a significant, extensible open-source resource for the Rydberg community, enabling efficient modeling of interactions in complex environments relevant to quantum simulation and sensing. The modular architecture and reported computational improvements are clear strengths that facilitate community extensions and practical use.

major comments (2)
  1. [§5] §5 (Stark map comparison): The sole experimental benchmark is the single-atom Stark map of ^{174}Yb, which validates only the MQDT component. No direct experimental or independent numerical comparison is provided for two-atom interaction energies under the static Green's tensor approximation in arbitrary geometries or near surfaces, leaving the central generality claim for pair potentials dependent on an unverified assumption.
  2. [§3.2] §3.2 (Green's tensor implementation): The adoption of frequency-independent static Green's tensors for interaction calculations is presented without quantitative assessment of the validity range or potential errors from neglecting dynamic effects or higher-multipole contributions, which is load-bearing for the surface-modified and arbitrary-geometry claims.
minor comments (2)
  1. [§4] The speedup claim of 'one order of magnitude' should be supported by explicit timing tables or figures specifying hardware, problem sizes, and baseline comparisons to allow quantitative assessment.
  2. [§2] Notation for MQDT channels and the definition of the interaction Hamiltonian could be clarified with an explicit table of symbols to improve readability for readers unfamiliar with the prior literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the work's significance. We address each major comment below, proposing targeted revisions where appropriate to strengthen the manuscript while maintaining its focus as a software implementation paper.

read point-by-point responses

  1. Referee: §5 (Stark map comparison): The sole experimental benchmark is the single-atom Stark map of ^{174}Yb, which validates only the MQDT component. No direct experimental or independent numerical comparison is provided for two-atom interaction energies under the static Green's tensor approximation in arbitrary geometries or near surfaces, leaving the central generality claim for pair potentials dependent on an unverified assumption.

    Authors: We agree that the presented experimental validation focuses on the MQDT single-atom description. The Green's tensor formalism for pair interactions follows a well-established approach in the Rydberg literature, with prior validations for free-space cases. In the revised manuscript, we will add a new subsection in §5 comparing computed free-space pair potentials to analytical dipole-dipole and van der Waals expressions as well as to independent numerical results from other codes. We acknowledge that new experimental data for surface-modified or arbitrary-geometry interactions lies beyond the scope of this theoretical and software-focused work. revision: partial

  2. Referee: §3.2 (Green's tensor implementation): The adoption of frequency-independent static Green's tensors for interaction calculations is presented without quantitative assessment of the validity range or potential errors from neglecting dynamic effects or higher-multipole contributions, which is load-bearing for the surface-modified and arbitrary-geometry claims.

    Authors: We thank the referee for this observation. The revised manuscript will expand §3.2 with a dedicated paragraph providing quantitative estimates: the static approximation holds when interatomic distances are much smaller than the wavelength of relevant Rydberg transitions (typically valid for blockade radii), with error bounds derived from the retardation parameter. Higher-multipole corrections (quadrupole etc.) are shown to be suppressed by factors of order (n² a₀ / R) for typical separations, supporting the dipole approximation used. These additions will directly address the validity range for the claimed geometries. revision: yes

Circularity Check

1 steps flagged

Minor self-citation to prior software; central framework uses established MQDT and Green's tensors without reduction to self-defined inputs

specific steps
  1. self citation load bearing [Abstract]
    "We implement this framework in an updated version of the open-source PairInteraction software [Weber et al., J.~Phys.~B~50 (2017)]."

    This is a self-citation to prior work by co-author Sebastian Weber, but the citation supports only the software implementation details rather than any load-bearing theoretical step; the MQDT and Green's tensor components are drawn from external literature and do not reduce to this citation.

full rationale

The derivation relies on standard multi-channel quantum defect theory (MQDT) parameters drawn from prior literature and the static electromagnetic Green's tensor formalism, both independent of the present work. The only self-citation is to the original PairInteraction software paper for the implementation update; this does not bear the load of any core theoretical claim or prediction. No equation reduces a result to a fitted parameter defined by the paper itself, and no uniqueness theorem or ansatz is smuggled via self-citation. The Stark-map comparison is external validation, not a circular fit.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard MQDT for divalent atoms and the static Green's tensor formalism; no new free parameters are introduced beyond those already established in the literature for the example atoms.

axioms (2)
  • domain assumption Multi-channel quantum defect theory accurately describes Rydberg states of divalent atoms such as strontium and ytterbium
    Invoked in the unified theoretical framework section as the basis for single-atom properties.
  • domain assumption Static electromagnetic Green's tensors provide a general description of interactions between two Rydberg atoms in arbitrary geometries including surface modifications
    Stated as the approach for calculating pair interactions.

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Reference graph

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