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REVIEW 2 major objections 4 minor 38 references

The most accurate interspecies frequency ratio involving a transportable clock is measured at 4.3 × 10^-18, demonstrating reproducible 10^-18-level operation.

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2026-08-04 18:15 UTC pith:SD43GRNL

load-bearing objection A new best value for the Yb+ E3 / Sr ratio at 4.3e-18 from a transportable Sr clock, with a caveat about the lattice shift model difference. the 2 major comments →

arxiv 2608.01916 v1 pith:SD43GRNL submitted 2026-08-03 physics.atom-ph quant-ph

Interspecies clock comparison below 5 times 10⁻¹⁸ uncertainty with a transportable clock

Chetan Vishwakarma , Ingo Nosske , Tim L\"ucke , Martin Steinel , Melina Filzinger , Erik Benkler , S\"oren D\"orscher , Nils Huntemann
show 1 more author
Christian Lisdat
This is my paper
classification physics.atom-ph quant-ph
keywords frequency ratiooptical lattice clocktransportable clockytterbium ion clockE3 transitioninterspecies comparisonlattice light shiftredefinition of second
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper reports the most accurate frequency ratio yet measured between two different atomic species when one of the clocks is transportable. The ratio between the ytterbium ion's octupole transition and strontium's clock transition is determined with fractional uncertainty 4.3 × 10^-18, improving on the previous best by a factor of 3.5. Four measurement campaigns across nearly two years, including physical transport and off-site operation of the strontium lattice clock, give statistically consistent results. This demonstrates that a transportable optical lattice clock can reproduce its frequency at the 10^-18 level, a requirement for its use in chronometric geodesy and as a transfer standard for inter-institute comparisons.

Core claim

The authors determine the optical frequency ratio νYb+/νSr = 1.495 991 618 544 900 588 1(65) with fractional uncertainty 4.3 × 10^-18. This is the most accurate interspecies clock comparison involving a transportable clock and one of the few measurements meeting the roadmap requirement of below 5 × 10^-18 for the redefinition of the SI second. The result is derived from a weighted average of four campaigns, whose means differ by no more than 3 × 10^-18 from the overall average, demonstrating reproducible operation of the transportable clock after transport and operational breaks. The authors also update the lattice light shift evaluation of the strontium clock using a single E1 magic frequen

What carries the argument

The measurement chain connects each clock's laser to a common ultrastable reference laser via an optical frequency comb, allowing a phase-coherent comparison of the two clock transitions. The transportable strontium clock's lattice light shift is evaluated using a measured E1 magic frequency νE1 = 368 554 463.4(1.7) MHz, assumed reproducible across campaigns, with the lattice laser detuning measured per campaign. The ytterbium ion clock operates on the electric-octupole transition with a systematic uncertainty of 2.7 × 10^-18. A covariance-based weighted average combines the four campaigns, treating systematic errors as fully correlated.

Load-bearing premise

The strontium clock's lattice light shift is computed from a single measured E1 magic frequency that is assumed not to change when the clock is transported or over time; all campaigns rely on this fixed value rather than per-campaign lattice shift determinations.

What would settle it

Re-determine νE1 independently at a later campaign (or after a transport) and compare it to 368 554 463.4 MHz. If the difference exceeds the 1.7 MHz uncertainty, the fixed-magic-frequency assumption fails and the reported 4.3 × 10^-18 total uncertainty would need revision. A direct interleaved two-trap-depth measurement at a remote site would also test the prediction.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • The transportable clock can act as a transfer standard for inter-institute clock comparisons without optical fiber links.
  • The measured ratio provides a benchmark that can link the two existing clusters of sub-5×10^-18 clock comparisons, e.g., by measuring the 27Al+/171Yb+ ratio.
  • The result supports the conclusion that a 2022 comparison suffered an uncontrolled ~10^-16-level frequency error, affecting current recommended frequency values.
  • Demonstrated reproducibility enables chronometric leveling at the centimeter uncertainty level.

Where Pith is reading between the lines

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

  • If the E1 magic frequency reproducibility holds for future transports, transportable clocks could omit per-campaign lattice shift calibrations, shortening remote measurement campaigns.
  • The consistency across four campaigns suggests that operational magic intensity techniques may be robust enough for other lattice clock species.
  • A future measurement of νYb+/νSr after a longer idle period, or with a second transportable clock, would test whether the 1.7 MHz reproducibility bound is a hard floor or can be lowered further.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper reports a determination of the optical frequency ratio between the 171Yb+ E3 transition at 642 THz and the 87Sr clock transition at 429 THz, using the stationary Yb1E3 single-ion clock and the transportable Sr4 lattice clock at PTB. The measurement spans four campaigns over nearly two years, with Sr4 occasionally transported and operated off-site. The ratio is measured phase-coherently via an optical frequency comb referenced to a common ultrastable laser. The final result is R = 1.495 991 618 544 900 588 1(65), with a fractional uncertainty of 4.3 × 10^-18, a factor 3.5 improvement over the previous best. The campaign results are statistically consistent (daily reduced chi-squared 1.19), and the uncertainty budget combines statistics, Yb1E3 systematics, Sr4 systematics, and gravitational redshift. The Sr4 systematic is dominated by the lattice light shift, now evaluated using a global E1 magic frequency νE1 = 368 554 463.4(1.7) MHz that is assumed reproducible across transports.

Significance. If the quoted uncertainty is sound, this measurement is the most accurate interspecies frequency comparison involving a transportable clock to date, and one of only a few below 5 × 10^-18 that meet the roadmap requirement for optical redefinition of the second. The paper's strengths are the direct phase-coherent measurement chain, the explicit per-campaign uncertainty budget, the covariance treatment of correlated systematics, and the demonstration of long-term reproducibility after transportation. Those features make the work valuable for chronometric geodesy and for linking clock clusters. The central uncertainty claim, however, rests critically on the Sr4 lattice light shift evaluation, whose model choice introduces a possible bias that is not currently included in the uncertainty budget.

major comments (2)
  1. [Supplemental Material, 'Determination of the E1 magic frequency in 87Sr'; Table I] Table I quotes a total fractional uncertainty of 4.3 × 10^-18, dominated by the Sr4 systematic contribution of 2.6 × 10^-18. The lattice light shift is evaluated using the global νE1 value. The supplement states explicitly that 'the lattice light shifts differ by no more than 4.5 × 10^-18 between this approach and the per-campaign approach [20]'. This difference is larger than the quoted total uncertainty and larger than the individual lattice-light-shift uncertainties (1.3–2.8 × 10^-18). Because the per-campaign method was used in the previous work and is not demonstrated to be invalid, the choice between the two methods changes the central value by more than the claimed uncertainty. The paper needs either a quantitative justification for preferring the global method, or a conservative systematic term covering the model difference. The statement 'at the level of the lattice light shift
  2. [Supplemental Material, 'Determination of the E1 magic frequency in 87Sr'] The global νE1 is derived from only three internal measurements with χ2_red = 1.6 (p = 0.16). The authors scale the uncertainties by sqrt(χ2_red), but this does not protect against a common-mode bias in the analysis, which they themselves identify as a plausible explanation (e.g., atomic temperature determination). Such a common-mode bias would shift the weighted mean νE1 and hence the lattice light shift for all campaigns without increasing the reported error. A sensitivity analysis or an explicit additional uncertainty for this bias is needed to support the 4.3 × 10^-18 claim.
minor comments (4)
  1. [Abstract] Typographical issue: 'below5 × 10−18' is missing a space; should read 'below 5 × 10−18'.
  2. [Figure 1] The axis labels and tick labels in the figure are garbled, e.g., '4/20230 3/20241 0/20240 2/2025'. Please ensure the final figure has clean month/year labels.
  3. [Figure 2] The legend/figure text repeats 'Ref. [29], 2025' twice; the labels should distinguish the two measurements. Also, the sentence about point colors before 2026 is difficult to parse.
  4. [Table I] The symbol eR is used in the table header but is not defined in the main text until later; consider defining it at first use.

Circularity Check

0 steps flagged

No circularity: ratio is directly measured via phase-coherent comb; systematic calibrations are independent of the target value.

full rationale

The central result R is obtained by comparing each clock's laser to a common ultrastable laser via one frequency comb branch, phase-coherently, directly measuring the ratio (main text, 'The frequency ratio of the two clocks is determined...'). No parameter is fitted to R: the weighted average uses covariances from systematic uncertainties, and the weights are chosen from those uncertainty estimates, not from the observed Ri. The global E1 magic frequency νE1 is a separately calibrated systematic parameter estimated from interleaved lattice-depth self-comparisons (Supplemental Material); its use to correct the same campaigns' data is a standard systematic evaluation, not a fit of the frequency ratio. The paper explicitly reports that the global-νE1 and per-campaign lattice-shift evaluations differ by up to 4.5e-18, which is an uncertainty/model-consistency concern, not a circular definition. Self-citations (Refs. [16,20,29]) describe apparatus and prior comparisons but are not load-bearing for the central claim; the result is benchmarked against external CIPM values and independent NPL/PTB/SYRTE measurements. No equation equates R to an input or redefines the target as a fitting parameter.

Axiom & Free-Parameter Ledger

1 free parameters · 4 axioms · 0 invented entities

The paper introduces no new physical entities. The result is an experimental measurement, and the main inputs are the systematic uncertainty budgets of the two clocks (one prior, one re-evaluated here) and a geometric redshift correction. The only data-derived numerical choice is the set of campaign weights in the weighted average, which is standard statistics and does not bias the central value beyond its quoted uncertainty.

free parameters (1)
  • Campaign weights w_i = [~0, 0.22, 0.16, 0.63]
    Weights assigned to campaigns C0-C3 in the weighted average, determined by minimizing u(R) using the estimated covariance matrix. This data-adaptive choice gives negligible weight to C0 because of its larger systematic uncertainty; it affects the final value at the ~1e-18 level, well within the total uncertainty.
axioms (4)
  • domain assumption The E1 magic frequency νE1 = 368 554 463.4(1.7) MHz is reproducible across campaigns and after transportation, so the lattice light shift can be evaluated from the known detuning of the lattice laser from this global value.
    Invoked in the Supplemental Material 'Determination of the E1 magic frequency in 87Sr'. The reduced Sr4 systematic uncertainty (2.6e-18) and thus the central uncertainty claim depend on this.
  • domain assumption Systematic frequency shifts of both clocks and the redshift correction are constant or fully correlated between campaigns, as encoded in the covariance matrix for the weighted average.
    Stated in the main text: 'the covariances introduced by systematic effects are treated as fully correlated between campaigns.' If this is wrong, the combined uncertainty could be mis-estimated.
  • domain assumption The previously characterized systematic uncertainty of the Yb1E3 clock (2.7e-18) is valid for the E3 transition operation during these measurements.
    Taken from Refs [18,19]; the paper does not re-derive it here. It is a standard metrological input from prior work.
  • domain assumption The optical frequency comb and the shared ultrastable laser link introduce negligible phase noise or systematic offset at the stated level.
    The comparison scheme is described in the main text and relies on Ref [25] for end-to-end topology. The paper states this suppresses excess noise between comb ports, but the absolute validity at 10^-19 level is assumed.

pith-pipeline@v1.3.0-daily-deepseek · 11675 in / 17295 out tokens · 171013 ms · 2026-08-04T18:15:02.866700+00:00 · methodology

0 comments
read the original abstract

We report a measurement of the optical frequency ratio between the $^2\mathrm{S}_{1/2}(F=0)$--${^2\mathrm{F}_{7/2}(F=3)}$ electric-octupole (E3) transition of $^{171}$Yb$^{+}$ and the $^1\mathrm{S}_0$--${^3\mathrm{P}_0}$ transition of $^{87}$Sr, $\nu_{\mathrm{Yb}^{+}}/\nu_\mathrm{Sr} = 1.495\,991\,618\,544\,900\,588\,1(65)$. Reaching a fractional uncertainty of $4.3 \times 10^{-18}$, this result improves upon the previous best by more than a factor of three and is among the few that meet the requirements for interspecies clock comparisons specified by the roadmap towards the redefinition of the SI second. The comparison is between a transportable optical lattice clock and a stationary single-ion clock. It spans a period of nearly two years, during which the transportable clock was intermittently operated off-campus. The ratio was reproducibly measured during four separate campaigns, which are consistent within their statistical uncertainties. The results demonstrate reproducible $10^{-18}$ level operation of the transportable clock and thus validate its application for chronometric geodesy and as a transfer standard for inter-institute clock comparisons, e.g., in the absence of optical fiber links.

Figures

Figures reproduced from arXiv: 2608.01916 by Chetan Vishwakarma, Christian Lisdat, Erik Benkler, Ingo Nosske, Martin Steinel, Melina Filzinger, Nils Huntemann, S\"oren D\"orscher, Tim L\"ucke.

Figure 1
Figure 1. Figure 1: FIG. 1. Results of the comparisons between the Yb1E3 single-ion clock and the Sr4 transportable optical lattice clock at PTB. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Overview of measured values of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

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Reference graph

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