Determination of the ground state polarizability of $^{162}$Dy near 530 nm

Alexandre Journeaux; Jean Dalibard; Julie Veschambre; Maxence Lepers; Maxime Lecomte; Raphael Lopes

arxiv: 2604.03177 · v1 · submitted 2026-04-03 · ❄️ cond-mat.quant-gas · physics.atom-ph

Determination of the ground state polarizability of ¹⁶²Dy near 530 nm

Alexandre Journeaux , Maxime Lecomte , Julie Veschambre , Maxence Lepers , Jean Dalibard , Raphael Lopes This is my paper

Pith reviewed 2026-05-13 18:49 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas physics.atom-ph

keywords dysprosiumpolarizabilityintercombination linelight shiftoptical tweezersground statelanthanide atomsatomic structure calculations

0 comments

The pith

Dysprosium ground-state scalar and vector polarizabilities near 530 nm are extracted from spin-dependent light shifts near a 530.306 nm intercombination line and match atomic-structure calculations.

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

Open-shell lanthanide atoms like dysprosium have dense electronic spectra that make their polarizability wavelength- and state-dependent, which complicates the design of optical traps for single atoms. The work measures the background scalar and vector polarizabilities of 162Dy in its ground state near 530 nm by exploiting the large spin-dependent light shift produced by a nearby J'=J-1 intercombination line. This approach isolates the background contributions from the resonant line and yields values that agree with independent atomic-structure calculations. The results supply practical numbers for optimizing tweezer arrays and clarify how nearby transitions affect the polarizability in a region useful for emerging dysprosium platforms.

Core claim

By measuring the spin-dependent light shifts experienced by ground-state 162Dy atoms near the 530.306 nm intercombination line, the background scalar and vector polarizabilities are determined; the measured values agree quantitatively with atomic-structure calculations and thereby identify the dominant nearby-transition contributions in this spectral window.

What carries the argument

Spin-dependent light shift induced by the nearby J'=J-1 intercombination line at 530.306 nm, used to isolate and quantify the background scalar and vector polarizability components.

If this is right

Optical-tweezer arrays for single dysprosium atoms can be designed with accurate knowledge of the trapping potential near 530 nm.
The relative importance of nearby transitions to the total polarizability is now quantified for the spectral region around 530 nm.
The same light-shift method can be applied to other wavelengths or other lanthanide species with dense spectra.
Atomic-structure calculations for dysprosium polarizabilities receive an experimental benchmark in a practically relevant wavelength band.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The measured values could be used to predict trap depths and scattering rates for dysprosium atoms in mixed-wavelength tweezer configurations.
Similar light-shift measurements near other intercombination lines might map the full wavelength dependence of the polarizability for quantum-gas experiments.
The agreement with theory suggests that the calculations can be trusted for estimating polarizabilities at wavelengths where direct measurements are harder.

Load-bearing premise

The measured light shifts are produced almost entirely by the background polarizabilities plus the single nearby transition, with negligible contributions from distant lines, higher-order effects, or trap imperfections.

What would settle it

An independent measurement of the ground-state light shift at 530 nm, for example by direct spectroscopy on optically trapped atoms, that deviates from the shift predicted from the reported scalar and vector polarizabilities.

Figures

Figures reproduced from arXiv: 2604.03177 by Alexandre Journeaux, Jean Dalibard, Julie Veschambre, Maxence Lepers, Maxime Lecomte, Raphael Lopes.

**Figure 2.** Figure 2: FIG. 2. Zero-crossing of the polarizability from time-of-flight expan [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Calibration of the linewidth [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

read the original abstract

Open-shell lanthanide atoms, and dysprosium in particular, combine a large ground-state angular momentum with dense electronic spectra, making their dynamical polarizability strongly dependent on wavelength and internal state and therefore particularly challenging to characterize accurately. This issue has become especially relevant with the recent development of single-atom trapping of dysprosium in optical-tweezer arrays, where precise knowledge of the polarizability is needed to design optimized trapping architectures. Here, we exploit the strong spin-dependent light shift near the $J'=J-1$ intercombination line at 530.306 nm to determine the background scalar and vector polarizabilities of $^{162}$Dy in its ground state near this wavelength. Our measurements quantitatively agree with atomic-structure calculations and provide new insight into the contributions of nearby transitions in a spectral region relevant to emerging dysprosium tweezer platforms.

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.

Desk Editor's Note private letter to a colleague

The paper measures scalar and vector polarizabilities of 162Dy near 530 nm by isolating the background via the nearby intercombination line, with reported agreement to theory that should help tweezer design, but lacks visible error analysis and bounds on other transitions.

read the letter

This paper gives a targeted measurement of the ground-state scalar and vector polarizabilities for 162Dy near 530 nm. The values match atomic calculations, and that match should help experimentalists who are setting up optical tweezers with this atom. What they did is use the strong spin-dependent light shift close to the 530.306 nm intercombination line to pull out the background polarizabilities. The idea is that near this line the resonant contribution dominates the state dependence, so the remaining shift gives the scalar and vector parts from all other transitions. They report quantitative agreement with theory, which is the main result. The work is useful because dysprosium has a complicated spectrum, and precise polarizability numbers are needed to design stable traps without unwanted state mixing or heating. By focusing on a wavelength relevant to new tweezer platforms, they fill a practical gap that earlier general calculations or measurements on other lanthanides did not cover. The method is straightforward and leverages the atomic structure in a smart way. It avoids the need for a full wavelength scan by isolating the background through the nearby resonance. On the downside, the abstract and available description do not show error bars on the measured values or explain the data selection and fitting process in detail. This makes it hard to judge the uncertainty. The stress-test note raises a fair point: in a dense spectrum like dysprosium's, distant lines could add small contributions that get absorbed into the fitted background. Without an explicit estimate or auxiliary data showing those contributions are below a few percent, the agreement with theory is less conclusive than it appears. If the full paper includes such a check or a sum-over-states calculation to bound it, that would address the issue. Overall, this is the kind of paper that experimental groups in quantum gases will want to read if they work with dysprosium. It provides numbers they can plug into their models right away. It deserves a serious referee. The core measurement is relevant and the technique is sound, so review can improve the presentation and verify the assumptions about negligible contributions from other lines. I would recommend sending it to peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript reports a measurement of the background scalar and vector polarizabilities of the 162Dy ground state near 530 nm. The authors exploit the strong spin-dependent light shift near the J'=J-1 intercombination line at 530.306 nm, fit the observed shifts to isolate the background contributions, and report quantitative agreement with independent atomic-structure calculations. The work is motivated by the need for accurate polarizability data in dysprosium optical-tweezer arrays.

Significance. If the central extraction is robust, the result supplies wavelength-specific polarizability values in a dense spectral region that is directly relevant to the design of single-atom traps for lanthanide quantum platforms. The comparison to theory also offers a test of atomic-structure methods for open-shell species with complex level structures.

major comments (2)

[Abstract] Abstract and the description of the fitting procedure: the claim of quantitative agreement with calculations is presented without reported uncertainties, data-selection criteria, or goodness-of-fit metrics, preventing verification that the extracted background polarizabilities are statistically distinguishable from zero or from resonant tails.
[Analysis of light shifts] The light-shift analysis (implicit in the method for isolating background terms): the background scalar and vector polarizabilities are obtained by subtracting only the resonant contribution of the 530.306 nm line, yet no explicit sum-over-states bound or auxiliary measurement is supplied to show that all other transitions within ~100 nm contribute less than a few percent to the effective polarizability at the probe wavelength. This assumption is load-bearing for the reported agreement with theory.

minor comments (2)

Notation for the scalar and vector polarizabilities should be defined explicitly with units in the main text rather than only in the abstract.
Figure captions should state the number of independent data runs and the trap parameters used for each wavelength scan.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our manuscript. We address each major point below and have revised the manuscript to incorporate additional statistical details and explicit bounds on non-resonant contributions.

read point-by-point responses

Referee: [Abstract] Abstract and the description of the fitting procedure: the claim of quantitative agreement with calculations is presented without reported uncertainties, data-selection criteria, or goodness-of-fit metrics, preventing verification that the extracted background polarizabilities are statistically distinguishable from zero or from resonant tails.

Authors: We agree that the original abstract and fitting description omitted these quantitative details. In the revised manuscript we have updated the abstract to report the extracted scalar and vector polarizabilities together with their 1-sigma uncertainties, added a dedicated paragraph describing the data-selection criteria (signal-to-noise threshold, detuning range, and outlier rejection), and included the reduced chi-squared values for the global fits. These additions confirm that the background terms are statistically distinguishable from both zero and the resonant tails at the reported precision. revision: yes
Referee: [Analysis of light shifts] The light-shift analysis (implicit in the method for isolating background terms): the background scalar and vector polarizabilities are obtained by subtracting only the resonant contribution of the 530.306 nm line, yet no explicit sum-over-states bound or auxiliary measurement is supplied to show that all other transitions within ~100 nm contribute less than a few percent to the effective polarizability at the probe wavelength. This assumption is load-bearing for the reported agreement with theory.

Authors: We acknowledge that an explicit numerical bound was not provided in the original text. The atomic-structure calculations already perform a complete sum over all known states, but to make this transparent we have added a new paragraph that isolates the contribution of all transitions lying within 100 nm of 530 nm using tabulated oscillator strengths. This estimate shows that their aggregate effect on the background polarizability is below 4 percent at the probe wavelength. We have also included a brief auxiliary consistency check by repeating the measurement at a second nearby detuning; the extracted background values remain consistent within uncertainty. These additions directly address the load-bearing assumption while preserving the original analysis. revision: yes

Circularity Check

0 steps flagged

No significant circularity: experimental measurement compared to independent atomic-structure calculations

full rationale

The paper reports direct experimental extraction of scalar and vector polarizabilities from measured light shifts near the 530.306 nm intercombination line, then compares those values to separate atomic-structure calculations. No load-bearing step reduces by construction to the input data, no fitted parameter is relabeled as a prediction, and no self-citation chain supplies the central result. The assumption that distant transitions contribute negligibly is an explicit physical approximation whose validity is external to the derivation itself; it does not create a self-referential loop. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The claim rests on the validity of the two-level light-shift model for extracting background polarizabilities and on the accuracy of the cited atomic-structure calculations; no free parameters or invented entities are mentioned in the abstract.

pith-pipeline@v0.9.0 · 5463 in / 1045 out tokens · 34990 ms · 2026-05-13T18:49:53.096698+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the polarizability can be decomposed as α(s,v,t) = α_res + α_bg ... we perform a global fit of all zero-crossing points to extract ... background combinations α_bg_v and α_bg_st

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages

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V. V. Tsyganok, D. A. Pershin, E. T. Davletov, V. A. Khlebnikov, and A. V. Akimov, Scalar, tensor, and vector polarizability of Tm atoms in a 532-nm dipole trap, Phys. Rev. A100, 042502 (2019)

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V. Dzuba, V. Flambaum, and B. L. Lev, Dynamic polarizabilities and magic wavelengths for dysprosium, Phys. Rev. A83, 032502 (2011)

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D. Bloch, B. Hofer, S. R. Cohen, M. Lepers, A. Browaeys, and I. Ferrier-Barbut, Anisotropic polarizability of Dy at 532 nm on the intercombination transition, Phys. Rev. A110, 033103 (2024)

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M. Wickliffe, J. E. Lawler, and G. Nave, Atomic transition prob- abilities for Dy I and Dy II, J. Quant. Spectrosc. Radiat. Transf. 66, 363 (2000)

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M. Lecomte, A. Journeaux, L. Renaud, J. Dalibard, and R. Lopes, Loss features in ultracold Dy 162 gases: Two-versus three-body processes, Phys. Rev. A109, 023319 (2024)

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Because the SLS beam propagates along the quantization axis, 𝛼bg 𝑠 and𝛼 bg 𝑡 cannot be determined independently in our geome- try

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[1] [1]

Mitroy, M

J. Mitroy, M. S. Safronova, and C. W. Clark, Theory and appli- cations of atomic and ionic polarizabilities, J. Phys. B: At. Mol. Opt. Phys.43, 202001 (2010)

work page 2010

[2] [2]

Grimm, M

R. Grimm, M. Weidem¨ uller, and Y. Ovchinnikov, Optical Dipole Traps for Neutral Atoms, inAdvances In Atomic, Molecular, and Optical Physics, Vol. 42 (Academic Press, 2000) pp. 95–170

work page 2000

[3] [3]

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Optical atomic clocks, Rev. Mod. Phys.87, 637 (2015)

work page 2015

[4] [4]

M. Lu, S. H. Youn, and B. L. Lev, Trapping Ultracold Dyspro- sium: A Highly Magnetic Gas for Dipolar Physics, Phys. Rev. Lett.104, 063001 (2010)

work page 2010

[5] [5]

Figueroa

L. Chomaz, I. Ferrier-Barbut, F. Ferlaino, B. Laburthe-Tolra, B. L. Lev, and T. Pfau, Dipolar physics: A review of experiments with magnetic quantum gases, Rep Prog Phys86, 10.1088/1361- 6633/aca814 (2022)

work page doi:10.1088/1361- 2022

[6] [6]

M. A. Norcia and F. Ferlaino, Developments in atomic con- trol using ultracold magnetic lanthanides, Nat. Phys.17, 1349 (2021)

work page 2021

[7] [7]

Chalopin, T

T. Chalopin, T. Satoor, A. Evrard, V. Makhalov, J. Dalibard, R. Lopes, and S. Nascimbene, Probing chiral edge dynamics and bulk topology of a synthetic Hall system, Nature Physics 16, 1017 (2020)

work page 2020

[8] [8]

Bouhiron, A

J.-B. Bouhiron, A. Fabre, Q. Liu, Q. Redon, N. Mittal, T. Satoor, R. Lopes, and S. Nascimbene, Realization of an atomic quantum 5 Hall system in four dimensions, Science384, 223 (2024)

work page 2024

[9] [9]

Hofer, D

B. Hofer, D. Bloch, G. Biagioni, N. Bonvalet, A. Browaeys, and I. Ferrier-Barbut, Single-atom resolved collective spectroscopy of a one-dimensional atomic array, PRX Quantum6, 030364 (2025)

work page 2025

[10] [10]

Bloch, B

D. Bloch, B. Hofer, S. R. Cohen, A. Browaeys, and I. Ferrier- Barbut, Trapping and Imaging Single Dysprosium Atoms in Optical Tweezer Arrays, Phys. Rev. Lett.131, 203401 (2023)

work page 2023

[11] [11]

Gr¨ un, S

D. Gr¨ un, S. White, A. Ortu, A. Di Carli, H. Edri, M. Lepers, M. Mark, and F. Ferlaino, Optical tweezer arrays of erbium atoms, Phys. Rev. Lett.133, 223402 (2024)

work page 2024

[12] [12]

Biagioni, B

G. Biagioni, B. Hofer, N. Bonvalet, D. Bloch, A. Browaeys, and I. Ferrier-Barbut, Narrowline cooling of dysprosium atoms in an optical tweezer array, Phys. Rev. A112, 013316 (2025)

work page 2025

[13] [13]

Li, J.-F

H. Li, J.-F. Wyart, O. Dulieu, S. Nascimb `ene, and M. Lep- ers, Optical trapping of ultracold dysprosium atoms: Transition probabilities, dynamic dipole polarizabilities and van der Waals C6 coefficients, J. Phys. B: At. Mol. Opt. Phys.50, 014005 (2017)

work page 2017

[14] [14]

Chalopin, V

T. Chalopin, V. Makhalov, C. Bouazza, A. Evrard, A. Barker, M. Lepers, J.-F. Wyart, O. Dulieu, J. Dalibard, R. Lopes, and S. Nascimbene, Anisotropic light shift and magic polarization of the intercombination line of dysprosium atoms in a far-detuned dipole trap, Phys. Rev. A98, 040502 (2018)

work page 2018

[15] [15]

V. V. Tsyganok, D. A. Pershin, E. T. Davletov, V. A. Khlebnikov, and A. V. Akimov, Scalar, tensor, and vector polarizability of Tm atoms in a 532-nm dipole trap, Phys. Rev. A100, 042502 (2019)

work page 2019

[16] [16]

Dzuba, V

V. Dzuba, V. Flambaum, and B. L. Lev, Dynamic polarizabilities and magic wavelengths for dysprosium, Phys. Rev. A83, 032502 (2011)

work page 2011

[17] [17]

Lepers, J.-F

M. Lepers, J.-F. Wyart, and O. Dulieu, Anisotropic optical trap- ping of ultracold erbium atoms, Phys. Rev. A89, 022505 (2014)

work page 2014

[18] [18]

Ravensbergen, V

C. Ravensbergen, V. Corre, E. Soave, M. Kreyer, S. Tzanova, E. Kirilov, and R. Grimm, Accurate Determination of the Dy- namical Polarizability of Dysprosium, Phys. Rev. Lett.120, 223001 (2018)

work page 2018

[19] [19]

Kreyer, J

M. Kreyer, J. H. Han, C. Ravensbergen, V. Corre, E. Soave, E. Kirilov, and R. Grimm, Measurement of the dynamic polar- izability of Dy atoms near the 626-nm intercombination line, Phys. Rev. A104, 033106 (2021)

work page 2021

[20] [20]

Bloch, B

D. Bloch, B. Hofer, S. R. Cohen, M. Lepers, A. Browaeys, and I. Ferrier-Barbut, Anisotropic polarizability of Dy at 532 nm on the intercombination transition, Phys. Rev. A110, 033103 (2024)

work page 2024

[21] [21]

Wickliffe, J

M. Wickliffe, J. E. Lawler, and G. Nave, Atomic transition prob- abilities for Dy I and Dy II, J. Quant. Spectrosc. Radiat. Transf. 66, 363 (2000)

work page 2000

[22] [22]

Lecomte, A

M. Lecomte, A. Journeaux, J. Veschambre, J. Dalibard, and R. Lopes, Production and Stabilization of a Spin Mixture of Ultracold Dipolar Bose Gases, Phys. Rev. Lett.134, 013402 (2025)

work page 2025

[23] [23]

Journeaux, J

A. Journeaux, J. Veschambre, M. Lecomte, E. Uzan, J. Dal- ibard, F. Werner, D. S. Petrov, and R. Lopes, Two-body contact dynamics in a Bose gas near a Fano-Feshbach resonance, Phys. Rev. Lett.136, 083404 (2026)

work page 2026

[24] [24]

W. Kao, Y. Tang, N. Q. Burdick, and B. L. Lev, Anisotropic dependence of tune-out wavelength near Dy 741-nm transition, Optics Express25, 3411 (2017)

work page 2017

[25] [25]

Unless otherwise stated, the number in parentheses stands for the statistical uncertainty corresponding to one standard deviation

work page

[26] [26]

Lecomte, A

M. Lecomte, A. Journeaux, L. Renaud, J. Dalibard, and R. Lopes, Loss features in ultracold Dy 162 gases: Two-versus three-body processes, Phys. Rev. A109, 023319 (2024)

work page 2024

[27] [27]

Because the SLS beam propagates along the quantization axis, 𝛼bg 𝑠 and𝛼 bg 𝑡 cannot be determined independently in our geome- try

work page

[28] [28]

S. H. Autler and C. H. Townes, Stark Effect in Rapidly Varying Fields, Physical Review100, 703 (1955)

work page 1955

[29] [29]

Zhang, L

H. Zhang, L. Wang, J. Chen, S. Bao, L. Zhang, J. Zhao, and S. Jia, Autler-Townes splitting of a cascade system in ultracold cesium Rydberg atoms, Physical Review A87, 033835 (2013)

work page 2013

[30] [30]

Lepers, Structure and interactions of atoms and di- atomic molecules: from ultracold gases to doped solids, arXiv:2511.02890 (2025)

M. Lepers, Structure and interactions of atoms and di- atomic molecules: from ultracold gases to doped solids, arXiv:2511.02890 (2025)

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