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arxiv: 2606.04997 · v2 · pith:XQRKQDVQnew · submitted 2026-06-03 · ⚛️ physics.atom-ph · nucl-ex· quant-ph

A thorium-229 optical nuclear clock with feedback loop

L. Toscani De Col , T. Riebner , I. Morawetz , F. Schneider , N. Sempelmann , J. Schlachet-L\'epinay , F. Schaden , M. Bartokos
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G. A. Kazakov K. Beeks B. Gerstenecker M. Pimon S. Lahs A. Hellerschmied T. Lercher J. Premper A. Niessner M. Matus H. Denker M. Cizek O. Cip V. Lal G. Zitzer V. Petrov J. Tiedau M. V. Okhapkin E. Peik T. Schumm
This is my paper

Pith reviewed 2026-06-28 02:35 UTC · model grok-4.3

classification ⚛️ physics.atom-ph nucl-exquant-ph
keywords thorium-229nuclear clockoptical clockabsorption spectroscopyultralight dark matterfrequency instabilitycalcium fluoride
0
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The pith

Stabilizing a laser to the thorium-229 nuclear transition inside a crystal creates a nuclear optical clock with shot-noise-limited stability reaching 10^{-15} over a day.

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

The paper demonstrates a working nuclear clock based on the 148 nm transition in thorium-229 embedded in a CaF2 crystal at room temperature. They lock a continuous-wave laser to the nuclear transition using a feedback loop based on continuous absorption spectroscopy. The clock is compared to a ytterbium ion clock and shows instability that scales as 3·10^{-12} √(τ/s), reaching 10^{-15} over a day. This performance is used to constrain ultralight dark matter models by searching for variations in the nuclear transition energy on timescales from 20 s to 1 day.

Core claim

The thorium-229 nuclear clock is implemented by stabilizing a continuous-wave laser to the 148 nm nuclear transition with rapid feedback based on continuous absorption spectroscopy in a millimeter-sized room temperature calcium fluoride crystal, showing a fractional frequency instability of 3·10^{-12} √(τ/s) and applied to constrain ultralight dark matter.

What carries the argument

The rapid feedback loop using continuous absorption spectroscopy to lock the laser to the thorium-229 nuclear transition.

If this is right

  • The nuclear clock enables tests of fundamental physics with enhanced sensitivity from the nuclear transition.
  • Future improvements could reduce instability by several orders of magnitude in solid-state nuclear clocks.
  • The dark matter constraints on couplings to photons, strong force, and quarks are competitive with atomic clock results.
  • The solid-state approach allows continuous operation at room temperature without vacuum systems.

Where Pith is reading between the lines

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

  • This feedback method may allow nuclear clocks to be built more easily than traditional atomic clocks by using embedded nuclei.
  • The technique could be adapted to detect other signals like variations in fundamental constants on short time scales.
  • Differential measurements between this nuclear clock and atomic clocks could isolate effects specific to nuclear transitions.

Load-bearing premise

The continuous absorption spectroscopy feedback loop maintains lock to the nuclear transition without introducing frequency shifts or excess noise beyond the reported shot-noise limit, and observed variations are not due to unaccounted systematics.

What would settle it

A measurement showing that the frequency instability does not follow the reported shot-noise scaling of 3·10^{-12} √(τ/s) or that dark matter constraints are inconsistent with other experiments due to systematics in the crystal or laser system.

Figures

Figures reproduced from arXiv: 2606.04997 by A. Hellerschmied, A. Niessner, B. Gerstenecker, E. Peik, F. Schaden, F. Schneider, G. A. Kazakov, G. Zitzer, H. Denker, I. Morawetz, J. Premper, J. Schlachet-L\'epinay, J. Tiedau, K. Beeks, L. Toscani De Col, M. Bartokos, M. Cizek, M. Matus, M. Pimon, M. V. Okhapkin, N. Sempelmann, O. Cip, S. Lahs, T. Lercher, T. Riebner, T. Schumm, V. Lal, V. Petrov.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: , the deviations δfi of the line centers from the frequency average of all five measurements differ by up to 1.7 kHz between datasets, which is well above the 0.13 kHz spread expected from statistical fluctuations in our measurement, but within the uncertainty reported in previous studies of the line center reproducibility [14]. Remeasuring at the same crystal position (see scans 2 and 4 in [PITH_FULL_IMA… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

The laser-accessible nuclear transition in the thorium-229 isotope has been identified as a promising candidate for the realization of an optical nuclear clock. Such a nuclear clock might rival or outperform current optical clocks based on electron-shell transitions in atoms or ions, is expected to be more robust against external perturbations, and provides enhanced sensitivity in clock-based tests of fundamental principles of physics. Here, we implement a thorium-229 nuclear clock by stabilizing a continuous-wave laser to the 148 nm nuclear transition with rapid feedback based on continuous absorption spectroscopy. The thorium-229 nuclei are embedded into a millimeter-sized, room temperature calcium fluoride crystal. A subharmonic of the 148 nm radiation is continuously compared to a Yb+ single-ion clock. The nuclear clock shows a simple shot-noise limited scaling of the fractional frequency instability of $3\cdot 10^{-12} \sqrt{\tau/\text{s}}$ where $\tau$ is the averaging time, approaching $10^{-15}$ instabilities over 1 day of continuous operation. Improvements of the instability by several orders of magnitude can be projected for future solid-state nuclear clocks. We use the nuclear clock to constrain models of ultralight dark matter by searching for periodic fluctuations and slow drifts in the nuclear transition energy, on time scales between 20 s and 1 day. Drawing benefit from the enhanced sensitivity of the thorium-229 transition, these constraints compete with the best atomic clocks concerning dark matter coupling to photons and go beyond previous measurements regarding coupling to the strong force and quarks.

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

1 major / 1 minor

Summary. The paper reports implementation of a thorium-229 nuclear clock by locking a continuous-wave laser to the 148 nm nuclear transition in 229Th nuclei embedded in a room-temperature CaF2 crystal, using rapid feedback from continuous absorption spectroscopy. A subharmonic of the laser is compared to an independent Yb+ single-ion clock. The nuclear clock exhibits shot-noise-limited fractional frequency instability scaling as 3·10^{-12} √(τ/s) and is used to constrain ultralight dark matter models via searches for periodic fluctuations and drifts in the transition frequency over timescales from 20 s to 1 day.

Significance. If the central performance claims hold after correction, this constitutes the first demonstration of a continuously operated solid-state nuclear clock with feedback stabilization, providing a new platform with potential robustness advantages over atomic clocks and competitive sensitivity for tests of fundamental physics including dark matter couplings to photons, the strong force, and quarks. The projected improvements and DM constraints add value.

major comments (1)
  1. [Abstract] Abstract: The stated instability scaling '3·10^{-12} √(τ/s)' is inconsistent both with standard shot-noise-limited behavior (which scales as 1/√τ, decreasing with averaging time) and with the claimed performance of approaching 10^{-15} at 1 day (τ=86400 s yields ~8.8×10^{-10} under the given formula). This is load-bearing for the performance and DM-search claims and requires explicit correction or clarification of the formula and supporting data.
minor comments (1)
  1. [Abstract] The abstract provides limited detail on the full error budget, statistical analysis of the instability data, or quantitative assessment of potential systematics in the feedback loop and crystal environment that could affect the lock or introduce frequency shifts.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for identifying the inconsistency in the reported instability scaling. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The stated instability scaling '3·10^{-12} √(τ/s)' is inconsistent both with standard shot-noise-limited behavior (which scales as 1/√τ, decreasing with averaging time) and with the claimed performance of approaching 10^{-15} at 1 day (τ=86400 s yields ~8.8×10^{-10} under the given formula). This is load-bearing for the performance and DM-search claims and requires explicit correction or clarification of the formula and supporting data.

    Authors: We agree that the scaling as written in the abstract is inconsistent with standard shot-noise-limited behavior and with the claimed performance at long averaging times. This is the result of a typographical error: the correct expression is 3·10^{-12} / √(τ/s). With the corrected formula, the instability at τ=86400 s is approximately 1.02×10^{-14}, consistent with the stated approach to 10^{-15} over one day. The underlying data, analysis, and figures in the manuscript support the corrected scaling. We will revise the abstract and any other occurrences of the formula. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental results are independently benchmarked

full rationale

The central results are direct experimental measurements: laser stabilization via continuous absorption spectroscopy in a Th-229 doped crystal, with frequency instability obtained by continuous comparison against an independent Yb+ single-ion clock. The reported shot-noise scaling and 10^{-15} level are presented as observed performance from that comparison, not derived from a fit to the target quantity itself. Dark-matter constraints arise from post-processing the measured frequency time series for periodic or drift signals; no parameter is fitted to the DM result and then re-used as a prediction. No self-citation chain, uniqueness theorem, or ansatz is invoked to justify the core claims. The derivation chain is therefore self-contained against external references and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on established properties of the thorium-229 transition and standard experimental techniques in atomic physics; no new entities or free parameters are introduced in the abstract.

axioms (2)
  • domain assumption The 148 nm transition in thorium-229 is a nuclear transition accessible by laser excitation.
    This is the foundational property enabling the clock, established in prior literature.
  • domain assumption The Yb+ single-ion clock provides a stable reference for comparison.
    Standard assumption in clock comparisons.

pith-pipeline@v0.9.1-grok · 5955 in / 1475 out tokens · 64086 ms · 2026-06-28T02:35:14.166905+00:00 · methodology

discussion (0)

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Forward citations

Cited by 4 Pith papers

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

  1. Generation of continuous-wave laser light at 148.4 nm using cavity-enhanced second harmonic generation in $BaMgF_4$

    physics.optics 2026-06 unverdicted novelty 7.0

    First experimental generation of 148.4 nm CW VUV laser light via cavity-enhanced SHG in BaMgF4 crystal, yielding 16 pW output power.

  2. Record nonlinear conversion efficiency in the production of high spectral purity vacuum ultraviolet laser at 148 nm

    physics.optics 2026-06 unverdicted novelty 6.0

    Demonstration of record conversion efficiency for a 148 nm VUV frequency comb using 16th-harmonic generation in a bulk-grown QPM crystal.

  3. Colloquium: Nuclear clocks

    physics.atom-ph 2026-06 unverdicted novelty 2.0

    Colloquium overview of Th-229 nuclear clock development, covering its nuclear physics basis, recent direct laser excitation, clock design and systematics in traps and solids, and sensitivity to fundamental constant va...

  4. The $^{229}$Th Isomer: Nuclear Structure, Clocks, and Tests of Fundamental Physics

    nucl-th 2026-06 unverdicted novelty 1.0

    Review of the 229Th isomer covering spectroscopy, nuclear structure models, and applications to fundamental physics tests.

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