Magnetic atoms with a large electric dipole moment

Boris G. Sartakov; Gerard Meijer; Giacomo Valtolina; Johannes Seifert; Sid C. Wright

arxiv: 2511.14225 · v2 · submitted 2025-11-18 · ⚛️ physics.atom-ph · cond-mat.quant-gas

Magnetic atoms with a large electric dipole moment

Johannes Seifert , Sid C. Wright , Boris G. Sartakov , Giacomo Valtolina , Gerard Meijer This is my paper

Pith reviewed 2026-05-17 21:09 UTC · model grok-4.3

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

keywords dysprosiumelectric dipole momentmetastable stateStark effectmicrowave spectroscopyopposite-parity doublet

0 comments

The pith

Dysprosium atoms can acquire an electric dipole moment exceeding one Debye in a long-lived metastable state.

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

The paper shows that a large electric dipole moment can be induced in dysprosium atoms held in a metastable state roughly 17513 cm inverse above the ground state. This state belongs to a strongly coupled opposite-parity doublet whose spacing of about 1.12 cm inverse is measured to kHz accuracy using microwave spectroscopy on an atomic beam. Stark shifts at low fields and optical spectra at high fields together give a reduced transition dipole moment of 7.65 Debye between the two levels. In strong electric fields the doublet mixes with a third state that connects to the ground state, allowing the metastable level to be populated by a single optical photon. The result supplies a concrete route to preparing atoms that carry substantial electric dipoles for controlled experiments.

Core claim

We experimentally show that an electric dipole moment of more than 1 Debye can be induced in the dysprosium atom, in a long-lived state that is about 17513 cm^{-1} above the ground state. This metastable state is part of a strongly coupled opposite-parity doublet. Using optically detected microwave spectroscopy in an atomic beam, we determine the approximately 1.12 cm^{-1} doublet spacing for the five stable bosonic isotopes of Dy with kHz-level accuracy. From the shift of the microwave transition frequency in low electric fields and from optical spectra in high electric fields, a reduced transition dipole moment of 7.65 Debye between the doublet states is extracted. In high electric fields,

What carries the argument

Strongly coupled opposite-parity doublet with reduced transition dipole moment of 7.65 Debye that mixes under electric fields to produce an induced dipole and couples to a third state for optical preparation.

If this is right

The metastable state can be populated via single-photon excitation from the ground state once a strong electric field mixes in the connecting level at 17727 cm inverse.
The doublet spacing is determined to kHz precision for each of the five stable bosonic isotopes.
The three-state interaction fully accounts for the spectra observed in fields up to 150 kV/cm.

Where Pith is reading between the lines

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

The approach could be transferred to other lanthanide atoms that have comparable dense spectra of opposite-parity levels near the ground state.
Prepared samples could be used to study many-body physics driven by long-range dipole-dipole forces in cold or trapped ensembles.
The spectroscopic precision might support future laboratory searches for slow drifts in fundamental constants.

Load-bearing premise

The observed Stark shifts at low fields and optical spectra at high fields arise purely from the identified doublet and its interaction with the third state, without significant contributions from field inhomogeneities or unaccounted mixing.

What would settle it

A direct measurement of the actual dipole moment through beam deflection in an inhomogeneous field or a clear deviation from the predicted Stark shift curve at intermediate field values would test the extracted 7.65 Debye value and the three-state model.

Figures

Figures reproduced from arXiv: 2511.14225 by Boris G. Sartakov, Gerard Meijer, Giacomo Valtolina, Johannes Seifert, Sid C. Wright.

**Figure 1.** Figure 1: FIG. 1. (a) Selected energy levels of Dy relevant for this study (not to scale). The quadratic (linear) shift of the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. Ionization detected microwave spectra of the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Measured excitation spectrum from [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

read the original abstract

We experimentally show that an electric dipole moment of more than 1 Debye can be induced in the dysprosium (Dy) atom, in a long-lived state that is about 17513 cm$^{-1}$ above the ground state. This metastable state is part of a strongly coupled opposite-parity doublet. Using optically detected microwave spectroscopy in an atomic beam, we determine the approximately 1.12 cm$^{-1}$ doublet spacing for the five stable bosonic isotopes of Dy with kHz-level accuracy. From the shift of the microwave transition frequency in low electric fields (below 150 V/cm) and from optical spectra in high electric fields (up to 150 kV/cm), a reduced transition dipole moment of 7.65 $\pm$ 0.05 Debye between the doublet states is extracted. In high electric fields the doublet interacts with a third state at 17727 cm$^{-1}$, that connects to the ground state via an electric-dipole transition. The three-state Stark interaction enables preparation of Dy atoms in the metastable state via single-photon excitation from the ground state.

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

This paper gives a new kHz-precise measurement of the Dy metastable doublet spacing and extracts a 7.65 D reduced dipole moment, with the main open question being whether low-field systematics are fully controlled.

read the letter

The main point is that they've found a metastable state in dysprosium with a large induced electric dipole moment of over 1 Debye, backed by a precise measurement of the opposite-parity doublet spacing. What the paper does well is the experimental part. They use optically detected microwave spectroscopy in an atomic beam to pin down the 1.12 cm^{-1} spacing to kHz accuracy for the bosonic isotopes. Then they extract the 7.65 Debye reduced dipole from the Stark shift in low fields and cross-check it with optical spectra in high fields up to 150 kV/cm. The consistency between those two regimes is a strength, and the note about the third state enabling single-photon preparation from the ground state adds practical value for loading into traps or beams. The data seem grounded in direct frequency measurements against standards and applied fields, with no obvious circularity. The soft spot is in the modeling assumptions for the dipole extraction. The low-field data fit assumes a clean two-level avoided crossing, but as the stress-test notes, field inhomogeneities could broaden or shift the observed kHz transitions, and the third state at 17727 cm^{-1} might contribute some mixing even below 150 V/cm. The paper mentions the three-state interaction mainly for high fields, so explicit quantification of those effects or upper limits on them would strengthen the ±0.05 D uncertainty. Without the full tables or detailed error budget, it's hard to judge how much that matters, but it's worth a closer look rather than a deal-breaker. This paper is for people in ultracold atomic physics working with dysprosium or similar lanthanides who need both magnetic and electric moments for interaction engineering. A reader looking for new spectroscopic constants or ways to prepare metastable states will get something out of it. It deserves a serious referee because the core measurement is new and the approach is direct. I would recommend putting it through peer review.

Referee Report

1 major / 2 minor

Summary. The manuscript reports an experimental demonstration that an electric dipole moment exceeding 1 Debye can be induced in a long-lived metastable state of dysprosium (approximately 17513 cm^{-1} above the ground state) that forms part of a strongly coupled opposite-parity doublet. Using optically detected microwave spectroscopy in an atomic beam, the authors measure the doublet spacing of ~1.12 cm^{-1} to kHz accuracy for the five stable bosonic isotopes. They extract a reduced transition dipole moment of 7.65 ± 0.05 Debye by analyzing the microwave transition shift in low electric fields (<150 V/cm) together with optical spectra in high fields (up to 150 kV/cm). At high fields the doublet interacts with a third state at 17727 cm^{-1}, enabling single-photon preparation of the metastable state from the ground state.

Significance. If the dipole-moment extraction holds, the result is significant because it identifies a concrete system in which a magnetic atom acquires a large, tunable electric dipole in a metastable state. This opens possibilities for combined magnetic-electric control in quantum gases or precision measurements. The use of two independent field regimes for cross-validation and the kHz-level frequency accuracy against external standards are clear strengths. The work also supplies a practical route to populate the metastable state.

major comments (1)

[Low-field Stark shift analysis] Low-field Stark-shift analysis (below 150 V/cm): The extraction of the 7.65 ± 0.05 Debye reduced dipole moment assumes that the observed kHz shifts arise purely from two-level avoided-crossing dynamics. Explicit quantitative bounds on electric-field inhomogeneity across the atomic beam and on second-order mixing with the third state at 17727 cm^{-1} are required; without them the stated uncertainty may be underestimated and the two-state model remains unverified at the precision claimed.

minor comments (2)

[Abstract and results section] Ensure that the precise measured doublet spacing (rather than the approximate value quoted in the abstract) is stated consistently in the main text and that any isotope dependence is tabulated.
[High-field optical spectra] In the high-field optical spectra, clarify the fitting procedure used to confirm the dipole moment once the three-state interaction is included.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. We appreciate the constructive feedback on the low-field analysis and address the major comment in detail below.

read point-by-point responses

Referee: [Low-field Stark shift analysis] Low-field Stark-shift analysis (below 150 V/cm): The extraction of the 7.65 ± 0.05 Debye reduced dipole moment assumes that the observed kHz shifts arise purely from two-level avoided-crossing dynamics. Explicit quantitative bounds on electric-field inhomogeneity across the atomic beam and on second-order mixing with the third state at 17727 cm^{-1} are required; without them the stated uncertainty may be underestimated and the two-state model remains unverified at the precision claimed.

Authors: We thank the referee for this helpful suggestion. While the two-level avoided-crossing model for the low-field microwave shifts is supported by the independent extraction of the same reduced dipole moment from the high-field optical spectra (where the three-state coupling to the level at 17727 cm^{-1} is explicitly included), we agree that explicit quantitative bounds would strengthen the presentation and better justify the quoted uncertainty. In the revised manuscript we will add a dedicated paragraph (in the results section or as a new methods subsection) providing these bounds from existing data and apparatus characterization. For field inhomogeneity, finite-element modeling of the electrode geometry combined with the measured atomic-beam divergence yields a maximum variation of <10 V/cm across the interaction volume at the low fields used, contributing <3 kHz to the transition-frequency uncertainty; this will be folded into the error budget. For second-order mixing with the third state, first-order perturbation theory using the measured 214 cm^{-1} separation and the dipole matrix elements determined from the high-field data shows a correction to the effective two-level dipole of <0.02 Debye below 150 V/cm, well below the stated 0.05 Debye uncertainty. These additions will be included in the revision. revision: yes

Circularity Check

0 steps flagged

No circularity in experimental extraction of induced dipole moment

full rationale

The paper reports direct measurements of microwave transition frequencies (kHz accuracy) and optical spectra in calibrated electric fields. The reduced dipole moment of 7.65 ± 0.05 D is obtained by fitting the low-field Stark shift of the microwave transition to the standard two-level avoided-crossing formula whose only free parameter is the transition dipole; this fit uses independent spectroscopic data and external frequency/field standards. High-field spectra are used only for cross-check and three-state modeling at >10 kV/cm, with no step redefining the target quantity in terms of itself or importing a load-bearing result solely via self-citation. The derivation chain is therefore self-contained against external benchmarks and does not reduce the reported >1 D induced moment to a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard atomic-physics assumptions about electric-dipole selection rules, the validity of the two-level Stark model at low fields, and the three-level mixing description at high fields; no new entities or ad-hoc parameters are introduced beyond the measured quantities themselves.

axioms (2)

standard math Electric-dipole selection rules govern the optical and microwave transitions between opposite-parity states.
Invoked implicitly when interpreting the observed Stark shifts and the single-photon excitation pathway.
domain assumption The low-field Stark shift is linear in the applied electric field for a permanent or induced dipole.
Used to extract the reduced transition dipole moment from the microwave frequency shift below 150 V/cm.

pith-pipeline@v0.9.0 · 5500 in / 1585 out tokens · 52122 ms · 2026-05-17T21:09:33.018170+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.

From the shift of the microwave transition frequency in low electric fields (below 150 V/cm) and from optical spectra in high electric fields (up to 150 kV/cm), a reduced transition dipole moment of 7.65 ± 0.05 Debye between the doublet states is extracted.

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.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Two-dimensional shelving spectroscopy of ultraviolet ground state transitions in dysprosium
physics.atom-ph 2026-04 unverdicted novelty 6.0

New measurements of UV ground-state transitions in dysprosium using shelving spectroscopy yield isotope shifts, hyperfine coefficients, and King plots that identify strong decay paths to a long-lived excited state.

Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages · cited by 1 Pith paper

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[1] [1]

Lahaye, C

T. Lahaye, C. Menotti, L. Santos, M. Lewenstein, and T. Pfau, The physics of dipolar bosonic quantum gases, Reports on Progress in Physics 72, 126401 (2009)

work page 2009

[2] [2]

M. A. Baranov, M. Dalmonte, G. Pupillo, and P. Zoller, Condensed matter theory of dipolar quantum gases, Chemical Reviews 112, 5012 (2012), pMID: 22877362

work page 2012

[3] [3]

C. M. Holland, Y. Lu, and L. W. Cheuk, On-demand entanglement of molecules in a reconfigurable optical tweezer array, Science 382, 1143 (2023)

work page 2023

[4] [4]

Y. Bao, S. S. Yu, L. Anderegg, E. Chae, W. Ketterle, K.-K. Ni, and J. M. Doyle, Dipolar spin-exchange and entanglement between molecules in an optical tweezer ar- ray, Science 382, 1138 (2023)

work page 2023

[5] [5]

L. R. B. Picard, A. J. Park, G. E. Patenotte, S. Gebret- sadkan, D. Wellnitz, A. M. Rey, and K.-K. Ni, Entangle- ment and iswap gate between molecular qubits, Nature 637, 821 (2025)

work page 2025

[6] [6]

D. K. Ruttley, T. R. Hepworth, A. Guttridge, and S. L. Cornish, Long-lived entanglement of molecules in magic- wavelength optical tweezers, Nature 637, 827 (2025)

work page 2025

[7] [7]

Micheli, G

A. Micheli, G. K. Brennen, and P. Zoller, A toolbox for lattice-spin models with polar molecules, Nature Physics 2, 341 (2006)

work page 2006

[8] [8]

Finelli, A

S. Finelli, A. Ciamei, B. Restivo, M. Schemmer, A. Cosco, M. Inguscio, A. Trenkwalder, K. Zaremba- Kopczyk, M. Gronowski, M. Tomza, and M. Zaccanti, Ultracold LiCr: A new pathway to quantum gases of paramagnetic polar molecules, PRX Quantum 5, 020358 (2024)

work page 2024

[9] [9]

S. Y. T. van de Meerakker, H. L. Bethlem, N. Vanhaecke, and G. Meijer, Manipulation and control of molecular beams, Chem. Rev. 112, 4828 (2012)

work page 2012

[10] [10]

Andreev, D

V. Andreev, D. G. Ang, D. DeMille, J. M. Doyle, G. Gabrielse, J. Haefner, N. R. Hutzler, Z. Lasner, C. Meisenhelder, B. R. O’Leary, C. D. Panda, A. D. West, E. P. West, X. Wu, and A. Collaboration, Improved limit on the electric dipole moment of the electron, Na- ture 562, 355 (2018)

work page 2018

[11] [11]

T. S. Roussy, L. Caldwell, T. Wright, W. B. Cairncross, Y. Shagam, K. B. Ng, N. Schlossberger, S. Y. Park, A. Wang, J. Ye, and E. A. Cornell, An improved bound on the electron’s electric dipole moment, Science 381, 46 (2023)

work page 2023

[12] [12]

Chomaz, I

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, Reports on Progress in Physics 86, 026401 (2022)

work page 2022

[13] [13]

B¨ ottcher, J.-N

F. B¨ ottcher, J.-N. Schmidt, M. Wenzel, J. Hertkorn, M. Guo, T. Langen, and T. Pfau, Transient supersolid properties in an array of dipolar quantum droplets, Phys. Rev. X 9, 011051 (2019)

work page 2019

[14] [14]

Tanzi, E

L. Tanzi, E. Lucioni, F. Fam` a, J. Catani, A. Fioretti, C. Gabbanini, R. N. Bisset, L. Santos, and G. Modugno, Observation of a dipolar quantum gas with metastable supersolid properties, Phys. Rev. Lett. 122, 130405 (2019)

work page 2019

[15] [15]

Chomaz, D

L. Chomaz, D. Petter, P. Ilzh¨ ofer, G. Natale, A. Traut- mann, C. Politi, G. Durastante, R. M. W. van Bijnen, A. Patscheider, M. Sohmen, M. J. Mark, and F. Ferlaino, Long-lived and transient supersolid behaviors in dipolar quantum gases, Phys. Rev. X 9, 021012 (2019)

work page 2019

[16] [16]

Budker, D

D. Budker, D. DeMille, E. D. Commins, and M. S. Zolo- torev, Investigation of nearly degenerate opposite parity states in atomic dysprosium, Phys. Rev. Lett. 70, 3019 (1993)

work page 1993

[17] [17]

B. M. Roberts, V. A. Dzuba, and V. V. Flambaum, Par- ity and time-reversal violation in atomic systems, Annual Review of Nuclear and Particle Science 65, 63 (2015)

work page 2015

[18] [18]

J. F. Wyart, Interpretation du spectre de dy i: I. ´Etude des configurations impaires, Physica 75, 371 (1974)

work page 1974

[19] [19]

Lepers, H

M. Lepers, H. Li, J.-F. Wyart, G. Qu´ em´ ener, and O. Dulieu, Ultracold rare-earth magnetic atoms with an electric dipole moment, Phys. Rev. Lett. 121, 063201 (2018)

work page 2018

[20] [20]

Mishra, L

C. Mishra, L. Santos, and R. Nath, Self-bound doubly dipolar bose-einstein condensates, Phys. Rev. Lett. 124, 073402 (2020)

work page 2020

[21] [21]

Ghosh, C

R. Ghosh, C. Mishra, L. Santos, and R. Nath, Droplet arrays in doubly dipolar bose-einstein condensates, Phys. Rev. A 106, 063318 (2022). 6

work page 2022

[22] [22]

Anich, N

G. Anich, N. H¨ ollrigl, M. Kreyer, R. Grimm, and E. Kir- ilov, Comprehensive characterization of an apparatus for cold electromagnetic dysprosium dipoles, Phys. Rev. A 110, 023311 (2024)

work page 2024

[23] [23]

Ghosh, M

R. Ghosh, M. Ciardi, R. Nath, and F. Cinti, Path integral monte carlo study of a doubly dipolar bose gas, Phys. Rev. B 110, 014513 (2024)

work page 2024

[24] [24]

Langen, G

T. Langen, G. Valtolina, D. Wang, and J. Ye, Quantum state manipulation and cooling of ultracold molecules, Nature Physics 20, 702 (2024)

work page 2024

[25] [25]

W. C. Martin, R. Zalubas, and L. Hagan, Atomic Energy Levels - The Rare-Earth Elements (U.S. Department of Commerce / National Bureau of Standards, 1978)

work page 1978

[26] [26]

Truppe, S

S. Truppe, S. Marx, S. Kray, M. Doppelbauer, S. Hofs¨ ass, H. C. Schewe, N. Walter, J. P´ erez-R´ ıos, B. G. Sar- takov, and G. Meijer, Spectroscopic characterization of aluminum monofluoride with relevance to laser cooling and trapping, Phys. Rev. A 100, 052513 (2019)

work page 2019

[27] [27]

J. W. M. Dekker, P. F. A. Klinkenberg, and J. F. Langkemper, Optical isotope shifts and nuclear deforma- tion in dysprosium, Physica 39, 393 (1968)

work page 1968

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Karra, K

M. Karra, K. Sharma, B. Friedrich, S. Kais, and D. Her- schbach, Prospects for quantum computing with an array of ultracold polar paramagnetic molecules, The Journal of Chemical Physics 144, 094301 (2016)

work page 2016