Pith. sign in

REVIEW 3 major objections 2 minor 3 cited by

Three optical clock frequency ratios measured to below 3.2 × 10^-18, meeting a milestone precision for redefining the SI second.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 14:05 UTC pith:6QFBJKJ5

load-bearing objection Careful, state-of-the-art measurement whose quoted sub-3.2e-18 uncertainties rest on a no-constant-bias assumption that the 14-sigma Sr discrepancy makes doubtful. the 3 major comments →

arxiv 2512.21428 v2 pith:6QFBJKJ5 submitted 2025-12-24 physics.atom-ph quant-ph

Atomic clock frequency ratios with fractional uncertainty leq 3.2 times 10⁻¹⁸

Alexander Aeppli , Willa J. Arthur-Dworschack , Kyle Beloy , Caitlin M. Berry , Tobias Bothwell , Angela Folz , Tara M. Fortier , Tanner Grogan
show 19 more authors
Youssef S. Hassan Zoey Z. Hu David B. Hume Benjamin D. Hunt Kyungtae Kim Amanda Koepke Dahyeon Lee David R. Leibrandt Ben Lewis Andrew D. Ludlow Mason C. Marshall Nicholas V. Nardelli Harikesh Ranganath Daniel A. Rodriguez Castillo Jeffrey A. Sherman Jacob L. Siegel Suzanne Thornton William Warfield Jun Ye
This is my paper
classification physics.atom-ph quant-ph PACS 06.30.Ft
keywords optical atomic clocksfrequency ratiosSI second redefinitionstrontium clock frequencyultrastable laser referencephase-stabilized fiber linkquantum projection noisedark uncertainty
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.

This paper reports new, direct frequency-comparison measurements among three of the most precise optical atomic clocks: a single aluminum-ion clock and ytterbium and strontium optical lattice clocks. All three frequency ratios—Al+/Sr, Al+/Yb, and Yb/Sr—have total fractional uncertainties at or below 3.2 × 10^-18, with the smallest at 2.2 × 10^-18, making them the most precise direct optical clock ratios reported to date and meeting a 5 × 10^-18 threshold identified as a milestone for redefining the SI second. The key innovation is a common ultrastable optical reference, derived from a cryogenic silicon cavity and delivered to both laboratories over a phase-stabilized 3.6 km fiber link, which improves comparison stability by factors of two to three. The results, however, disagree with the same collaboration's 2021 measurements in the strontium-containing ratios by about 14 standard deviations, implying a roughly 1 × 10^-16 revision of the strontium clock frequency. The paper argues from a battery of systematics tests and an end-to-end network loopback that its new values are accurate, while conceding that the discrepancy is unresolved and needs independent cross-checks.

Core claim

On the paper's own terms: with all three clocks running simultaneously from January to March 2025, the collaboration measured the three ratios given in Eq. (1), with total fractional uncertainties of 2.2 × 10^-18 (Al+/Sr), 3.2 × 10^-18 (Al+/Yb), and 3.1 × 10^-18 (Yb/Sr). The Yb/Sr ratio instability reached 1.3 × 10^-16 at one second, and the Al+-involving ratios are limited by single-ion quantum projection noise at 3.9 × 10^-16; the common silicon-cavity reference reduces averaging time by roughly an order of magnitude compared with the previous campaign. The paper reports a 14-standard-deviation shift in the two ratios involving strontium relative to the 2021 values, corresponding to about

What carries the argument

The central mechanism is a phase-stabilized optical distribution network: a 1542 nm laser locked to a cryogenic single-crystal silicon cavity at one laboratory is sent over a 3.6 km fiber to the other laboratory, where it phase-locks each clock laser via frequency combs; a hydrogen-maser RF signal is multiplexed on the same fiber for a common microwave reference. This common reference suppresses the Dick effect and quantum projection noise, lowering the instability floor. The validity of the network is established by a loopback test that sends the silicon-cavity light to the second laboratory, uses it to lock a second comb, returns a 1397 nm laser, and compares the frequency-doubled light (6

Load-bearing premise

The analysis stands on the assumption that the new campaign's measurements are free of any unknown systematic bias — if a hidden offset affected the new data, the quoted sub-3.2 × 10^-18 uncertainties and the implied 1 × 10^-16 strontium revision are not reliable.

What would settle it

An independent measurement of these three ratios by a different laboratory, ideally using a different ultrastable reference and a different network path (or a satellite link), would settle the central claim: if it reproduces the new values, the 2021 campaign was biased; if it reproduces the 2021 values, the new campaign carries the hidden offset. A simpler first test is a direct optical comparison of a distant, independently evaluated strontium clock against the same aluminum-ion clock, without the shared fiber network.

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

If this is right

  • The three ratio values in Eq. (1) are, to the authors' knowledge, the most precise direct optical clock ratios published, with total fractional uncertainties of 2.2, 3.2, and 3.1 × 10^-18.
  • The measured precision meets the ≤5 × 10^-18 criterion identified by the community as a milestone for deciding whether to redefine the SI second.
  • The common silicon-cavity reference lowers the instability of the Yb/Sr ratio to 1.3 × 10^-16/√τ and of the Al+ ratios to 3.9 × 10^-16/√τ, a factor-of-3 improvement that cuts the time needed to reach a given statistical uncertainty by roughly a factor of ten.
  • The strontium-containing ratios imply the strontium clock frequency should be revised by about 1 × 10^-16 relative to the 2021 values; this revision would bring the measured ratios into agreement with the new data.
  • The Yb/Sr excess scatter (χ²_red = 6.4) shows that uncharacterized shifts remain in at least one lattice clock, and the paper states that repeatability below 1 × 10^-17 remains an outstanding issue for the redefinition effort.

Where Pith is reading between the lines

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

  • If the ~1 × 10^-16 strontium revision is confirmed by an independent group, the prior 2021 strontium evaluation most likely contained an unaccounted shift (e.g., in the blackbody radiation correction), rather than the new network; the revised value would become the de facto standard for strontium-based chronometric leveling and searches for time-variation of fundamental constants.
  • The 14σ disagreement between two campaigns that both claim sub-1 × 10^-17 accuracy is itself evidence that at least one of the two error budgets is incomplete; the paper's dark-uncertainty model absorbs day-to-day scatter but cannot absorb a constant offset, so the discrepancy cannot be resolved by re-weighting the data.
  • A testable extension: run one of the lattice clocks against two independent silicon cavities (or against a distant clock via satellite link) to separate network-origin from atom-origin offsets; the loopback used here covers only the two-laboratory fiber path.
  • The three-clocks-simultaneously design is the seed of a network-level metrology: with three-cornered hat analysis the paper already isolates per-clock stabilities, and with a multi-ion Al+ clock the same network could directly target the Yb/Sr between-day scatter.

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

3 major / 2 minor

Summary. The manuscript reports direct optical frequency ratio measurements between the 27Al+, 171Yb, and 87Sr clocks in the Boulder network, carried out on 13 days between January and March 2025. Using a cryogenic silicon cavity as a common reference distributed over a 3.6 km fiber link, the authors achieve fractional instabilities of a few times 10^-16/sqrt(τ) and quote total fractional uncertainties of 2.2×10^-18 (Al+/Sr), 3.2×10^-18 (Al+/Yb), and 3.1×10^-18 (Yb/Sr) after Bayesian aggregation. The paper emphasizes that this meets a 5×10^-18 roadmap milestone for the SI second, while also reporting large discrepancies with the BACON21 results, especially in the Sr-containing ratios (~1×10^-16, about 14σ). Extensive modulation tests, a new end-to-end network loopback, and multi-ratio analytics are presented to support the accuracy of the campaign.

Significance. If the quoted uncertainties are taken at face value, these are the most precise direct optical clock ratios yet reported and are relevant to the SI second redefinition process. The paper is notable for its transparency: it states the discrepancies with prior work, gives the full Bayesian model, reports alternative statistics, and includes modulation tests of several large systematic effects. The loopback measurement bounding the network at 0.9(1.6)×10^-19, the in-situ correction validations, and the three-cornered-hat analysis are commendable and strengthen the case that no single known systematic at the 10^-17 level is unaccounted for. However, the central claim of sub-3.2×10^-18 uncertainty is conditional on an unproven premise—the absence of any unknown constant systematic bias—and the unresolved 14σ Sr discrepancy makes this premise load-bearing rather than cosmetic.

major comments (3)
  1. [Supplement C, Comprehensive Bayesian model] The model encodes the assumption, explicitly stated in Supplement C, that 'the measurements themselves are free from any unknown systematic bias.' The systematic corrections are central (α,β,γ ~ N(0,1)) and the day-to-day dark-uncertainty terms are zero-mean (λ ~ N(0,ξ^2)). Such terms can inflate the reported uncertainty but cannot absorb a constant, campaign-wide offset. Given the ~1×10^-16 (14σ) discrepancy in both Sr-containing ratios, a constant bias in the present campaign is a viable explanation of the data. The abstract's statement that these measurements 'meet an important milestone criterion for redefinition of the second' therefore overstates the robustness of Eqs. (1). Please either add a global-offset parameter with a sensitivity analysis, or explicitly qualify the abstract and conclusion so that the quoted uncertainties are described as conditional on no uncharacterized comm
  2. [Main text, Discussion and Conclusion] The statement that 'all known systematic effects that shift any of the three clocks by 10^-17 or more have been tested' supports the individual corrections, but the discrepancy is an order of magnitude larger than the quoted uncertainties. The modulation tests cover known effects; they do not, and cannot, rule out a combination of smaller unknown effects or a single effect not included in the model. The conclusion already notes that repeatability below 10^-17 remains outstanding, but this caveat appears only after the central claims. Please add an explicit paragraph stating that the unresolved discrepancy could reside in the present campaign and discussing the consequences for the SI-redefinition roadmap. The accompanying Bayesian model should also be applied with a constant-offset scenario so readers can see how the quoted uncertainties change under that assumption.
  3. [Measurement results; Supplement C, dark uncertainty] The Yb/Sr ratio has χ2_red = 6.4, with between-day variability of 3.3(9)×10^-18. The Bayesian model accounts for this through zero-mean random effects (ξ). For 13 daily points, a time-correlated drift in the Yb/Sr residuals—for example from a slow environmental change or an operational parameter that evolves over the campaign—could bias the mean without violating the zero-mean assumption. Please report the daily residuals as a function of date, check for autocorrelation, and include a sensitivity test with a linear trend or an AR(1) term in the dark-uncertainty model. This directly affects the central value of Yb/Sr and the claimed 3.1×10^-18 uncertainty.
minor comments (2)
  1. [Main text, loopback description] The sentence in the Discussion says the loopback test evaluates 'every element from Si cavity to 87Sr atoms,' but the description shows the 698 nm comparison is made against the 87Sr clock laser 'picked off just before the atoms.' This is an overstatement; the loopback validates the network and laser delivery up to the atoms, not the atom-light interaction. Please rephrase to reflect the actual measurement point.
  2. [Fig. 2 caption] The caption refers to 'color filled points' and colored shaded regions but does not identify which color corresponds to which ratio. Please add a legend or explicit color definitions so the lower panel is interpretable.

Circularity Check

0 steps flagged

No significant circularity: the reported ratios are direct measurements; the self-citations are for comparison and modeling, not inputs that force the answer.

full rationale

The central claim is a set of measured frequency ratios (Eqs. 1), obtained by direct point-by-point division of clock frequencies from three simultaneously operated optical clocks, not by a model that presupposes the reported values. The Bayesian aggregation is fully described in Supplement C: observed daily ratios are modeled as centered on true ratios, with systematic corrections entering as a_i*alpha with alpha ~ N(0,1) and day-level 'dark uncertainty' lambda terms that are zero-mean. The priors for each mu are N(0, 10^-14), which is broad compared to the 10^-18 scale of the quoted uncertainties, and the paper states 'the result is not sensitive to the choice of prior distribution.' The reuse of the authors' earlier work is limited to the hierarchical model structure from BACON21 [11] and to BACON21/CIPM values used as comparison references; these are not data used to construct the new ratios. The retroactive adjustment of BACON21 values using updated Yb/Sr coefficients (footnote [37]) is a reanalysis of the old dataset and is not load-bearing for the new measurements, since the 1.5e-18 and 7.3e-18 shifts are far smaller than the ~1e-16 discrepancy discussed. The paper explicitly flags its main limitation in Supplement C: 'all models here incorporating dark uncertainty or between-day variability assume that this variability affects every measurement equally and that the measurements themselves are free from any unknown systematic bias.' This is an external-validity or correctness caveat, not a circularity: the ratios are independently measured, the network loopback gives an independent 0.9(1.6)e-19 bound, and the systematic modulations are direct experimental checks. No derivation step reduces to its own input or to a self-citation chain.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

The central claim rests primarily on measured systematics plus the no-unknown-bias assumption. No fitted parameter forces the target ratios, but the dark-uncertainty xi parameters and Yb lattice parameters are fitted in-service and affect the uncertainty budget or corrections.

free parameters (3)
  • Dark uncertainty xi for each clock = xi_Al = 2.3(1.7), xi_Yb = 2.0(1.2), xi_Sr = 2.2(1.2) (x10^-18)
    MCMC-estimated parameters in the Bayesian model absorb day-to-day excess scatter (Supplement C); they directly widen the reported ratio uncertainties.
  • Yb lattice light-shift parameters nu_E1 and beta = nu_E1 = 394798263.8(1.5) MHz, beta = -1.2(2)x10^-21
    Fitted to dedicated interleaved trap-depth measurements (Supplement G); used to correct the Yb lattice shift, a leading systematic. This is calibration fitting, not fitting of the target ratios.
  • Bayesian hyperpriors for xi and mu = xi prior: truncated normal mean 5e-15, std 1e-14; mu prior std 1e-14
    Chosen by hand, but the paper reports the result is insensitive to prior choice (Supplement C).
axioms (6)
  • domain assumption No unknown systematic bias in the current measurement campaign.
    Stated in Supplement C: all models 'assume ... measurements themselves are free from any unknown systematic bias.' The 14-sigma disagreement with BACON21 makes this the decisive fragility.
  • domain assumption The end-to-end loopback (Si cavity to NIST comb, back to JILA at 698 nm) is an upper bound on network error and instability.
    Used to assign network uncertainties sigma_N in Supplementary Table 1; assumes the round-trip path with two fibers bounds the one-way path.
  • domain assumption White frequency noise after the 100 s servo attack time and Allan deviation extrapolation give the daily statistical uncertainty.
    Main text Fig. 2(a); if residual non-white noise is present, the quoted statistical uncertainties are underestimated.
  • domain assumption NGS survey marker heights and their stability determine gravitational redshift between the clocks.
    Supplement B/E: height difference change <5 mm is below ratio uncertainty; used to correct geopotential shifts.
  • domain assumption Atomic coefficients (BBR, lattice polarizabilities, etc.) from prior literature are correct.
    Supplement E-G: e.g., the Sr BBR Einstein A coefficient update changes the correction by 7.3x10^-18; wrong coefficients would bias the ratios.
  • standard math Frequency comb measurement equation nu = m(n f_rep + f0 + f_b) + f_os with maser-referenced counters holds for all clocks.
    Supplement C, Refs. [33, 68].

pith-pipeline@v1.3.0-alltime-deepseek · 25697 in / 11950 out tokens · 121452 ms · 2026-08-03T14:05:36.652650+00:00 · methodology

0 comments
read the original abstract

We report high-precision frequency ratio measurements between optical atomic clocks based on $^{27}$Al$^+$, $^{171}$Yb, and $^{87}$Sr. With total fractional uncertainties at or below $3.2 \times 10^{-18}$, these measurements meet an important milestone criterion for redefinition of the second in the International System of Units. Discrepancies in $^{87}$Sr ratios at approximately $1\times10^{-16}$ and the Al$^+$/Yb ratio at $1.6\times10^{-17}$ in fractional units compared to our previous measurements underscore the importance of repeated, high-precision comparisons by different laboratories. A key innovation in this work is the use of a common ultrastable reference delivered to all clocks via a 3.6 km phase-stabilized fiber link between two institutions. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2 to 3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of $1.3 \times 10^{-16}$ at 1 second. By enabling faster comparisons, this stability will improve sensitivity to non-white noise processes and other underlying limits of state-of-the-art optical frequency standards.

Figures

Figures reproduced from arXiv: 2512.21428 by Alexander Aeppli, Amanda Koepke, Andrew D. Ludlow, Angela Folz, Benjamin D. Hunt, Ben Lewis, Caitlin M. Berry, Dahyeon Lee, Daniel A. Rodriguez Castillo, David B. Hume, David R. Leibrandt, Harikesh Ranganath, Jacob L. Siegel, Jeffrey A. Sherman, Jun Ye, Kyle Beloy, Kyungtae Kim, Mason C. Marshall, Nicholas V. Nardelli, Suzanne Thornton, Tanner Grogan, Tara M. Fortier, Tobias Bothwell, Willa J. Arthur-Dworschack, William Warfield, Youssef S. Hassan, Zoey Z. Hu.

Figure 1
Figure 1. Figure 1: FIG. 1. Simplified schematic of the Boulder optical clock net [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Frequency ratio measurement results. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Insights making use of three clocks running simulta [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: Point types distinguish measurement method [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Evolution of frequency ratio measurements. Asterisks (*) indicate the values we presented in BACON21 [7, 11, 34, 50– [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 3 Pith papers

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

  1. A thorium-229 optical nuclear clock with feedback loop

    physics.atom-ph 2026-06 unverdicted novelty 8.0

    A functional thorium-229 optical nuclear clock is demonstrated in a solid-state crystal with shot-noise limited performance and applied to dark matter constraints.

  2. International Optical Clock Comparison Using the European Optical Fiber Network

    physics.atom-ph 2026-04 unverdicted novelty 6.0

    International fiber-linked comparison of optical clocks achieves 7.7×10^{-18} agreement between independent ^{171}Yb^+ (E3) clocks at NPL and PTB, the first such verification below 10^{-17}.

  3. An Al$^+$ clock with $1.6\times10^{-18}$ systematic uncertainty and its frequency ratios

    physics.atom-ph 2026-06 unverdicted novelty 5.0

    An Al+ single-ion clock is evaluated at 1.6×10^{-18} systematic uncertainty with absolute frequency 1121015393207859.19(24) Hz and ratio to Sr clock of 2.611701431781462668(36).

Reference graph

Works this paper leans on

92 extracted references · cited by 3 Pith papers

  1. [1]

    Weyers, V

    S. Weyers, V. Gerginov, M. Kazda, J. Rahm, B. Lip- phardt, G. Dobrev, and K. Gibble, Metrologia 55, 789 (2018)

    2018

  2. [2]

    Gerginov, G

    V. Gerginov, G. W. Hoth, T. P. Heavner, T. E. Parker, K. Gibble, and J. A. Sherman, Metrologia 62, 035002 (2025)

    2025

  3. [3]

    Beattie, B

    S. Beattie, B. Jian, C. Marceau, K. Gibble, and M. Gertsvolf, Metrologia 62, 035003 (2025)

    2025

  4. [4]

    A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. Schmidt, Reviews of Modern Physics 87, 637–701 (2015)

    2015

  5. [5]

    Dimarcq, M

    N. Dimarcq, M. Gertsvolf, G. Mileti, S. Bize, C. W. Oates, E. Peik, D. Calonico, T. Ido, P. Tavella, F. Mey- nadier, G. Petit, G. Panfilo, J. Bartholomew, P. De- fraigne, E. A. Donley, P. O. Hedekvist, I. Sesia, M. Wouters, P. Dub´ e, F. Fang, F. Levi, J. Lodewyck, H. S. Margolis, D. Newell, S. Slyusarev, S. Weyers, J.-P. Uzan, M. Yasuda, D.-H. Yu, C. Rie...

    2024

  6. [6]

    Schioppo, J

    M. Schioppo, J. Kronj¨ ager, A. Silva, R. Ilieva, J. W. Paterson, C. F. A. Baynham, W. Bowden, I. R. Hill, R. Hobson, A. Vianello, M. Dovale-´Alvarez, R. A. Williams, G. Marra, H. S. Margolis, A. Amy-Klein, O. Lopez, E. Cantin, H. ´Alvarez Mart ´ ınez, R. Le Targat, P. E. Pottie, N. Quintin, T. Legero, S. H¨ afner, U. Sterr, R. Schwarz, S. D¨ orscher, C. ...

    2022

  7. [7]

    Grebing, A

    C. Grebing, A. Al-Masoudi, S. D¨ orscher, S. H¨ afner, V. Gerginov, S. Weyers, B. Lipphardt, F. Riehle, U. Sterr, 6 and C. Lisdat, Optica 3, 563 (2016)

    2016

  8. [8]

    Hachisu, F

    H. Hachisu, F. Nakagawa, Y. Hanado, and T. Ido, Scien- tific Reports 8, 4243 (2018)

    2018

  9. [9]

    J. Yao, J. A. Sherman, T. Fortier, H. Leopardi, T. Parker, W. McGrew, X. Zhang, D. Nicolodi, R. Fasano, S. Sch¨ affer, K. Beloy, J. Savory, S. Romisch, C. Oates, S. Diddams, A. Ludlow, and J. Levine, Physical Review Applied 12, 044069 (2019)

    2019

  10. [10]

    W. R. Milner, J. M. Robinson, C. J. Kennedy, T. Both- well, D. Kedar, D. G. Matei, T. Legero, U. Sterr, F. Riehle, H. Leopardi, T. M. Fortier, J. A. Sherman, J. Levine, J. Yao, J. Ye, and E. Oelker, Physical Review Letters 123, 173201 (2019)

    2019

  11. [11]

    Boulder Atomic Clock Optical Network (BACON) Col- laboration, Nature 591, 564 (2021)

    2021

  12. [12]

    H. N. Hausser, J. Keller, T. Nordmann, N. M. Bhatt, J. Kiethe, H. Liu, I. M. Richter, M. Von Boehn, J. Rahm, S. Weyers, E. Benkler, B. Lipphardt, S. D¨ orscher, K. Stahl, J. Klose, C. Lisdat, M. Filzinger, N. Huntemann, E. Peik, and T. E. Mehlst¨ aubler, Physical Review Letters 134, 023201 (2025)

    2025

  13. [13]

    M. S. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A. Derevianko, and C. W. Clark, Reviews of Modern Physics 90, 025008 (2018)

    2018

  14. [14]

    C. J. Kennedy, E. Oelker, J. M. Robinson, T. Bothwell, D. Kedar, W. R. Milner, G. E. Marti, A. Derevianko, and J. Ye, Physical Review Letters 125, 201302 (2020)

    2020

  15. [15]

    Filzinger, S

    M. Filzinger, S. D¨ orscher, R. Lange, J. Klose, M. Steinel, E. Benkler, E. Peik, C. Lisdat, and N. Huntemann, Phys- ical Review Letters 130, 253001 (2023)

    2023

  16. [16]

    Lange, N

    R. Lange, N. Huntemann, J. M. Rahm, C. Sanner, H. Shao, B. Lipphardt, C. Tamm, S. Weyers, and E. Peik, Physical Review Letters 126, 011102 (2021)

    2021

  17. [17]

    M. S. Safronova, Annalen der Physik 531, 1800364 (2019)

    2019

  18. [18]

    Sherrill, A

    N. Sherrill, A. O. Parsons, C. F. A. Baynham, W. Bow- den, E. Anne Curtis, R. Hendricks, I. R. Hill, R. Hob- son, H. S. Margolis, B. I. Robertson, M. Schioppo, K. Szymaniec, A. Tofful, J. Tunesi, R. M. Godun, and X. Calmet, New Journal of Physics 25, 093012 (2023)

    2023

  19. [19]

    Flury, Journal of Physics: Conference Series 723, 012051 (2016)

    J. Flury, Journal of Physics: Conference Series 723, 012051 (2016)

    2016

  20. [20]

    Grotti, I

    J. Grotti, I. Nosske, S. Koller, S. Herbers, H. Denker, L. Timmen, G. Vishnyakova, G. Grosche, T. Waterholter, A. Kuhl, S. Koke, E. Benkler, M. Giunta, L. Maisen- bacher, A. Matveev, S. D¨ orscher, R. Schwarz, A. Al- Masoudi, T. H¨ ansch, T. Udem, R. Holzwarth, and C. Lisdat, Phys. Rev. Appl. 21, L061001 (2024)

    2024

  21. [21]

    M. C. Marshall, D. A. R. Castillo, W. J. Arthur- Dworschack, A. Aeppli, K. Kim, D. Lee, W. Warfield, J. Hinrichs, N. V. Nardelli, T. M. Fortier, J. Ye, D. R. Leibrandt, and D. B. Hume, Phys. Rev. Lett. 135, 033201 (2025)

    2025

  22. [22]

    W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Sch¨ affer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, Nature564, 87 (2018)

    2018

  23. [23]

    Aeppli, K

    A. Aeppli, K. Kim, W. Warfield, M. S. Safronova, and J. Ye, Phys. Rev. Lett. 133, 023401 (2024)

    2024

  24. [24]

    See Supplemental Material at [URL Will Be Inserted by Publisher] for More Information

  25. [25]

    D. G. Matei, T. Legero, S. H¨ afner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, Physical Review Letters 118, 263202 (2017)

    2017

  26. [26]

    Oelker, R

    E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonder- house, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, Nature Photonics 13, 714 (2019)

    2019

  27. [27]

    Bressi, G

    G. Bressi, G. Carugno, F. Della Valle, G. Galeazzi, G. Ruoso, and G. Sartori, Physical Review A 83, 052101 (2011)

    2011

  28. [28]

    Van Dyke, BRAN Technical Information, 2004

    J. Van Dyke, BRAN Technical Information, 2004

    2004

  29. [29]

    Ye, J.-L

    J. Ye, J.-L. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L.-S. Ma, J. Opt. Soc. Am. B 20, 1459 (2003)

    2003

  30. [30]

    Narbonneau, M

    F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, Ch. Daussy, A. Amy-Klein, and Ch. Chardonnet, Review of Scientific Instruments 77, 064701 (2006)

    2006

  31. [31]

    N. V. Nardelli, H. Leopardi, T. R. Schibli, and T. M. Fortier, Laser & Photonics Reviews 17, 2200650 (2023)

    2023

  32. [32]

    T. M. Fortier, A. Bartels, and S. A. Diddams, Optics Letters 31, 1011–1013 (2006)

    2006

  33. [33]

    Fortier and E

    T. Fortier and E. Baumann, Communications Physics 2, 153 (2019)

    2019

  34. [34]

    Nemitz, T

    N. Nemitz, T. Ohkubo, M. Takamoto, I. Ushijima, M. Das, N. Ohmae, and H. Katori, Nature Photonics 10, 258–261 (2016)

    2016

  35. [35]

    Lindvall, M

    T. Lindvall, M. Pizzocaro, R. Godun, M. Abgrall, D. Akamatsu, A. Amy-Klein, E. Benkler, N. Bhatt, D. Calonico, E. Cantin, E. Cantoni, G. Cerretto, C. Chardonnet, M. A. C. Marin, C. Clivati, S. Condio, E. A. Curtis, H. Denker, S. Donadello, S. D¨ orscher, C.-H. Feng, M. Filzinger, T. Fordell, I. Goti, K. Hanhij¨ arvi, H. N. Hausser, I. Hill, K. Hosaka, N. ...

    2025

  36. [36]

    H. S. Margolis, G. Panfilo, G. Petit, C. Oates, T. Ido, and S. Bize, Metrologia 61, 035005 (2024)

    2024

  37. [37]

    The 171Yb frequency would de- crease by 1.5 × 10−18 [24]

    With improved evaluation of atomic coefficients, we can calculate the deviations from BACON21 by applying the corrections retroactively. The 171Yb frequency would de- crease by 1.5 × 10−18 [24]. The 87Sr frequency would de- crease by 7.3 × 10−18 [23]. This changes the deviations of the ratio values (BACON21 minus this work) in the units of their combined ...

  38. [38]

    Bothwell, D

    T. Bothwell, D. Kedar, E. Oelker, J. M. Robinson, S. L. Bromley, W. L. Tew, J. Ye, and C. J. Kennedy, Metrolo- gia 56, 065004 (2019)

    2019

  39. [39]

    Aeppli, A

    A. Aeppli, A. Chu, T. Bothwell, C. J. Kennedy, D. Kedar, P. He, A. M. Rey, and J. Ye, Science Advances 8, eadc9242 (2022)

    2022

  40. [40]

    S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C.-W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, Physical Review Letters 123, 033201 (2019). 7

    2019

  41. [41]

    S. M. Brewer, J.-S. Chen, K. Beloy, A. M. Hankin, E. R. Clements, C. W. Chou, W. F. McGrew, X. Zhang, R. J. Fasano, D. Nicolodi, H. Leopardi, T. M. Fortier, S. A. Diddams, A. D. Ludlow, D. J. Wineland, D. R. Leibrandt, and D. B. Hume, Physical Review A 100, 013409 (2019)

    2019

  42. [42]

    J. L. Siegel, in preparation (2025)

    2025

  43. [43]

    Koepke, T

    A. Koepke, T. Lafarge, A. Possolo, and B. Toman, Metrologia 54, S34 (2017)

    2017

  44. [44]

    Thompson and S

    M. Thompson and S. L. R. Ellison, Accreditation and Quality Assurance 16, 483–487 (2011)

    2011

  45. [45]

    Bodnar, R

    O. Bodnar, R. Nalule Muhumuza, and A. Possolo, Metrologia 57, 064004 (2020)

    2020

  46. [46]

    Notably, the JILA-NIST link was tested differently in the two campaigns: in BACON21, a loopback test was performed only at 1 .5 µm, including the 3.6-km link and NIST frequency combs but omitting elements solely at JILA, whereas in the current campaign, the test extends to 698 nm as shown in Fig. 3(b)

  47. [47]

    Gray and D

    J. Gray and D. Allan, in 28th Annual Symposium on Frequency Control(IEEE, Atlantic City, NJ, USA, 1974), pp. 243–246

    1974

  48. [48]

    4(b) around 104 s, where the model calculates an unphysical negative variance [47] and only an upper bound can be plotted

    See for example the missing points from Fig. 4(b) around 104 s, where the model calculates an unphysical negative variance [47] and only an upper bound can be plotted

  49. [49]

    M. E. Kim, W. F. McGrew, N. V. Nardelli, E. R. Clements, Y. S. Hassan, X. Zhang, J. L. Valencia, H. Leopardi, D. B. Hume, T. M. Fortier, A. D. Ludlow, and D. R. Leibrandt, Nature Physics 19, 25 (2023)

    2023

  50. [50]

    Akamatsu, M

    D. Akamatsu, M. Yasuda, H. Inaba, K. Hosaka, T. Tan- abe, A. Onae, and F.-L. Hong, Optics Express 22, 7898 (2014)

    2014

  51. [51]

    G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, Metrologia 45, 539 (2008)

    2008

  52. [52]

    Grotti, S

    J. Grotti, S. Koller, S. Vogt, S. H¨ afner, U. Sterr, C. Lis- dat, H. Denker, C. Voigt, L. Timmen, A. Rolland, F. N. Baynes, H. S. Margolis, M. Zampaolo, P. Thoumany, M. Pizzocaro, B. Rauf, F. Bregolin, A. Tampellini, P. Bar- bieri, M. Zucco, G. A. Costanzo, C. Clivati, F. Levi, and D. Calonico, Nature Physics 14, 437 (2018)

    2018

  53. [53]

    Hachisu, G

    H. Hachisu, G. Petit, F. Nakagawa, Y. Hanado, and T. Ido, Optics Express 25, 8511 (2017)

    2017

  54. [54]

    Kim, M.-S

    H. Kim, M.-S. Heo, W.-K. Lee, C. Y. Park, H.-G. Hong, S.-W. Hwang, and D.-H. Yu, Japanese Journal of Applied Physics 56, 050302 (2017)

    2017

  55. [55]

    Lemke, A

    N. Lemke, A. Ludlow, Z. Barber, T. Fortier, S. Did- dams, Y. Jiang, S. Jefferts, T. Heavner, T. Parker, and C. Oates, Physical Review Letters 103, 063001 (2009)

    2009

  56. [56]

    Lodewyck, S

    J. Lodewyck, S. Bilicki, E. Bookjans, J.-L. Robyr, C. Shi, G. Vallet, R. Le Targat, D. Nicolodi, Y. Le Coq, J. Gu´ ena, M. Abgrall, P. Rosenbusch, and S. Bize, Metrolo- gia 53, 1123 (2016)

    2016

  57. [57]

    W. F. McGrew, X. Zhang, H. Leopardi, R. J. Fasano, D. Nicolodi, K. Beloy, J. Yao, J. A. Sherman, S. A. Sch¨ affer, J. Savory, R. C. Brown, S. R¨ omisch, C. W. Oates, T. E. Parker, T. M. Fortier, and A. D. Ludlow, Optica 6, 448 (2019)

    2019

  58. [58]

    Pizzocaro, P

    M. Pizzocaro, P. Thoumany, B. Rauf, F. Bregolin, G. Mi- lani, C. Clivati, G. A. Costanzo, F. Levi, and D. Calonico, Metrologia 54, 102 (2017)

    2017

  59. [59]

    Rosenband, D

    T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Science 319, 1808 (2008)

    2008

  60. [60]

    Takamoto, I

    M. Takamoto, I. Ushijima, M. Das, N. Nemitz, T. Ohkubo, K. Yamanaka, N. Ohmae, T. Takano, T. Akat- suka, A. Yamaguchi, and H. Katori, Comptes Rendus. Physique 16, 489 (2015)

    2015

  61. [61]

    Fujieda, S.-H

    M. Fujieda, S.-H. Yang, T. Gotoh, S.-W. Hwang, H. Hachisu, H. Kim, Y. K. Lee, R. Tabuchi, T. Ido, W.- K. Lee, M.-S. Heo, C. Y. Park, D.-H. Yu, and G. Pe- tit, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 65, 973 (2018)

    2018

  62. [62]

    Hisai, D

    Y. Hisai, D. Akamatsu, T. Kobayashi, K. Hosaka, H. In- aba, F.-L. Hong, and M. Yasuda, Metrologia 58, 015008 (2021)

    2021

  63. [63]

    Pizzocaro, M

    M. Pizzocaro, M. Sekido, K. Takefuji, H. Ujihara, H. Hachisu, N. Nemitz, M. Tsutsumi, T. Kondo, E. Kawai, R. Ichikawa, K. Namba, Y. Okamoto, R. Takahashi, J. Komuro, C. Clivati, F. Bregolin, P. Barbieri, A. Mura, E. Cantoni, G. Cerretto, F. Levi, G. Maccaferri, M. Roma, C. Bortolotti, M. Negusini, R. Ricci, G. Zacchiroli, J. Roda, J. Leute, G. Petit, F. P...

    2021

  64. [64]

    Riehle, P

    F. Riehle, P. Gill, F. Arias, and L. Robertsson, Metrolo- gia 55, 188 (2018)

    2018

  65. [65]

    van Westrum, NOAA Technical Memorandum NOS NGS 77 (2019)

    D. van Westrum, NOAA Technical Memorandum NOS NGS 77 (2019)

    2019

  66. [66]

    L. O. Ohenhen, G. Zhai, J. Lucy, S. Werth, G. Carlson, M. Khorrami, F. Onyike, N. Sadhasivam, A. Tiwari, K. Ghobadi-Far, S. F. Sherpa, J.-C. Lee, S. Zehsaz, and M. Shirzaei, Nature Cities 2, 543–554 (2025)

    2025

  67. [67]

    van Westrum and K

    D. van Westrum and K. Ahlgren, NOAA Technical Mem- orandum NOS NGS 99 (2025)

    2025

  68. [68]

    frep is set by the comb lock to the Si cavity; f0 is controlled to a set value; and m and fos are set experimentally by each clock

    Atomic transition frequency values for each clock are ob- tained by combining a measured beatnote fb against a comb tooth n with the comb repetition rate frep, car- rier envelope offset f0, frequency multiplication factor m, and experimentally applied offsets fos. frep is set by the comb lock to the Si cavity; f0 is controlled to a set value; and m and fo...

  69. [69]

    Margolis and M

    H. Margolis and M. Pizzocaro, Guidelines on the Evalu- ation and Reporting of Correlation Coefficients between Frequency Ratio Measurements, 2020

    2020

  70. [70]

    D¨ orscher, N

    S. D¨ orscher, N. Huntemann, R. Schwarz, R. Lange, E. Benkler, B. Lipphardt, U. Sterr, E. Peik, and C. Lisdat, Metrologia 58, 015005 (2021)

    2021

  71. [71]

    Mandel and R

    J. Mandel and R. C. Paule, Analytical Chemistry 42, 1194 (1970)

    1970

  72. [72]

    Langan, J

    D. Langan, J. P. Higgins, D. Jackson, J. Bowden, A. A. Veroniki, E. Kontopantelis, W. Viechtbauer, and M. Sim- monds, Research Synthesis Methods 10, 83 (2019)

    2019

  73. [73]

    Merkatas, B

    C. Merkatas, B. Toman, A. Possolo, and S. Schlam- minger, Metrologia 56, 054001 (2019)

    2019

  74. [74]

    Possolo, Statistical Science 38, 655 (2023)

    A. Possolo, Statistical Science 38, 655 (2023)

    2023

  75. [75]

    K. Kim, A. Aeppli, T. Bothwell, and J. Ye, Physical Re- 8 view Letters 130, 113203 (2023)

    2023

  76. [76]

    Bothwell, C

    T. Bothwell, C. J. Kennedy, A. Aeppli, D. Kedar, J. M. Robinson, E. Oelker, A. Staron, and J. Ye, Nature 602, 420 (2022)

    2022

  77. [77]

    Lisdat, S

    Ch. Lisdat, S. D¨ orscher, I. Nosske, and U. Sterr, Physical Review Research 3, L042036 (2021)

    2021

  78. [78]

    Blatt, J

    S. Blatt, J. W. Thomsen, G. K. Campbell, A. D. Ludlow, M. D. Swallows, M. J. Martin, M. M. Boyd, and J. Ye, Phys. Rev. A 80, 052703 (2009)

    2009

  79. [79]

    Shi, J.-L

    C. Shi, J.-L. Robyr, U. Eismann, M. Zawada, L. Lorini, R. Le Targat, and J. Lodewyck, Phys. Rev. A 92, 012516 (2015)

    2015

  80. [80]

    Ushijima, M

    I. Ushijima, M. Takamoto, and H. Katori, Phys. Rev. Lett. 121, 263202 (2018)

    2018

Showing first 80 references.