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Cited by 727Advanced Frequency and Time StandardsRelativity and Gravitational TheoryNetwork Time Synchronization Technologies

Atomic clock performance enabling geodesy below the centimetre level

Open access
McGrew, W. F., Zhang, X., Fasano, R. J., Schäffer, S. A., Beloy, K., Nicolodi, D., Brown, R. C., Hinkley, N. +4 more·2018·Nature
DOI 10.1038/s41586-018-0738-2
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Abstract

The passage of time is tracked by counting oscillations of a frequency reference, such as Earth’s revolutions or swings of a pendulum. By referencing atomic transitions, frequency (and thus time) can be measured more precisely than any other physical quantity, with the current generation of optical atomic clocks reporting fractional performance below the 10−17 level1–5. However, the theory of relativity prescribes that the passage of time is not absolute, but is affected by an observer’s reference frame. Consequently, clock measurements exhibit sensitivity to relative velocity, acceleration and gravity potential. Here we demonstrate local optical clock measurements that surpass the current ability to account for the gravitational distortion of space-time across the surface of Earth. In two independent ytterbium optical lattice clocks, we demonstrate unprecedented values of three fundamental benchmarks of clock performance. In units of the clock frequency, we report systematic uncertainty of 1.4 × 10−18, measurement instability of 3.2 × 10−19 and reproducibility characterized by ten blinded frequency comparisons, yielding a frequency difference of [−7 ± (5)stat ± (8)sys] × 10−19, where ‘stat’ and ‘sys’ indicate statistical and systematic uncertainty, respectively. Although sensitivity to differences in gravity potential could degrade the performance of the clocks as terrestrial standards of time, this same sensitivity can be used as a very sensitive probe of geopotential5–9. Near the surface of Earth, clock comparisons at the 1 × 10−18 level provide a resolution of one centimetre along the direction of gravity, so the performance of these clocks should enable geodesy beyond the state-of-the-art level. These optical clocks could further be used to explore geophysical phenomena10, detect gravitational waves11, test general relativity12 and search for dark matter13–17. Improved techniques allow the measurement of a frequency difference with an uncertainty of the order of 10–19 between two independent atomic optical lattice clocks, suggesting that they may be able to improve state-of-the-art geodetic techniques.

AI snapshot

Written from the paper’s full text.

TL;DR

Two independent ytterbium optical lattice clocks achieved systematic uncertainty of 1.4 × 10⁻¹⁸, measurement instability of 3.2 × 10⁻¹⁹, and a ten-measurement blinded reproducibility of [−7 ± 5_stat ± 8_sys] × 10⁻¹⁹. The authors show that clock comparisons at the 1 × 10⁻¹⁸ level can provide 1 cm resolution along gravity, surpassing state-of-the-art geodetic techniques.

Key findings

  • Each clock reached a total systematic uncertainty of 1.4 × 10⁻¹⁸; measurement instability reached 3.2 × 10⁻¹⁹ by white-frequency-noise extrapolation, with 4.5 × 10⁻¹⁹ single-clock instability at 36 hours and 6.4 × 10⁻¹⁹ for unsynchronized Ramsey operation.
  • Ten blinded frequency comparisons over more than a month gave a frequency difference of [−7 ± (5)_stat ± (8)_sys] × 10⁻¹⁹ after correcting all relevant systematics.
  • Background-gas collision shifts were measured with coefficient −1.64(12) × 10⁻¹⁷ s, giving shifts of −5.5(5) × 10⁻¹⁸ for Yb-1 and −3.6(3) × 10⁻¹⁸ for Yb-2; spin-polarization impurity shift scaled as 5.50(12) × 10⁻¹⁷ × η, constraining the shift to <3 × 10⁻¹⁹ for Yb-1 and <1 × 10⁻¹⁹ for Yb-2.
  • Near Earth’s surface, relativistic effects are 1.1 × 10⁻¹⁸ per cm of vertical displacement, so 1 × 10⁻¹⁸ clock comparisons provide 1 cm gravity resolution; the TT redshift transformation uncertainty is 6 × 10⁻¹⁸, limited by several-centimetre geodetic determination.

Methods

  • ¹⁷¹Yb atoms were laser-cooled and loaded into two vertically oriented one-dimensional optical lattices near the magic wavelength λ_latt = 759 nm, at 50 E_r trap depth, with 5,000 atoms per clock, >99.5% spin polarization, and 500 nK longitudinal temperature.
  • Clock operation used 560 ms Rabi spectroscopy on the 578 nm transition with 1.4 Hz Fourier-limited FWHM, plus unsynchronized 510 ms Ramsey spectroscopy; comparisons used synchronous interrogation and a blinding protocol with a pseudorandom ±1 kHz offset.
  • Systematic uncertainty was evaluated via a full budget (Table 1), and geopotential determination used the Q407 marker, spirit levelling with gravimetry, and atomic height measured to 2 mm resolution.

Limitations

  • The paper states that transforming to the TT reference frame has 6 × 10⁻¹⁸ uncertainty, limited by several-centimetre-level geodetic determination, much larger than the clock comparison uncertainty; height uncertainty at or below 1 cm remains an optimistic goal.
  • The paper reports that one-second instability of 1.5 × 10⁻¹⁶ remains higher than the expected quantum-projection-noise limit (<5 × 10⁻¹⁷) due to technical noise, and one eleventh dataset was excluded by a white-frequency-noise post-selection criterion.
  • The paper notes that a faulty wire compromised Faraday shielding in Yb-2 during four early comparisons, causing a mid-10⁻¹⁸ DC Stark shift; more generally, the reproducibility campaign used two co-located clocks, and the text states that long-baseline or remote comparisons would be limited by gravitational knowledge.

Model-written summary. Check it against the paper before relying on it.

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Registry

Crossref · 10.1038/s41586-018-0738-2

Cites

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Claims the paper makes

0 of 40 cited sources checked · 0 supported · 0 flagged

  • Findingown data
    § Atomic clock performance beyond the geodetic limit · p. 7

    A weighted average of ten blinded frequency comparisons yields a frequency difference (ν2-ν1)/νclock = [-7±(5)stat±(8)sys] × 10^-19 after correcting for all relevant systematic effects.

    “A weighted average of these measurements leads to a frequency difference ( ν 2ν 1 )/ ν clock = [-7±(5)stat±(8)sys] × 10 -19 after correcting for all relevant systematic effects.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Atomic clock performance beyond the geodetic limit · p. 4

    The total systematic uncertainty is 1.4 × 10^-18 for each ytterbium optical lattice clock system.

    “We report a total uncertainty of 1.4 × 10 -18 for each system, as shown in Table 1.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Atomic clock performance beyond the geodetic limit · p. 4

    The fractional frequency shift from background gas collisions varies linearly with loss rate, with a coefficient of -1.64(12) × 10^-17 s.

    “As shown in Fig. 2a, the fractional frequency shift from background gas collisions is confirmed to vary linearly with loss rate, with a coefficient of -1.64(12) × 10 -17 s.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Atomic clock performance beyond the geodetic limit · p. 7

    An estimated measurement instability of 3.2 × 10^-19 is found by fitting a white frequency noise model to the total Allan deviation and extrapolating the fit to the full measurement time.

    “An estimated measurement instability of 3.2 × 10 -19 is found by fitting a white frequency noise model to the total Allan deviation and extrapolating the fit to the full measurement time.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Atomic clock performance beyond the geodetic limit · p. 2

    The authors demonstrate optical clock measurements surpassing the present-day ability to account for the gravitational distortion of space-time across the surface of Earth.

    “Here we demonstrate optical clock measurements surpassing the present-day ability to account for the gravitational distortion of space-time across the surface of Earth.”
    Quote in the paperSubstantial claim
  • May combine two claims. 48
  • Classified as probably not a substantial claim. 29
  • The quote only partly states this claim. 7

  • May combine two claims.

    Findingreasoning
    § Discussion. · p. 8

    The gravitational redshift listed in Table 1 is similar for each clock, since the two systems are closely located, leading to a small relative uncertainty.

    “We note that the gravitational redshift listed in Table 1 is similar for each clock, since the two systems are closely located, leading to a small relative uncertainty.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Atomic clock performance beyond the geodetic limit · p. 4

    Characteristic time constants for Yb-1 and Yb-2 are 3.0 s and 4.5 s, respectively.

    “Characteristic values of the time constant for Yb-1 and Yb-2 are 3.0 s and 4.5 s, respectively, and this value is measured every few days.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning
    § Methods. · p. 12

    The total environmental shift uncertainty is 4 × 10^-19 and 5 × 10^-19 for Yb-1 and Yb-2, respectively.

    “With these modifications, the total environmental shift uncertainty is 4 × 10 -19 and 5 × 10 -19 for Yb-1 and Yb-2, respectively.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Methods. · p. 12

    With BBR corrections properly applied, no noise floor is observed and the clocks average below 5 × 10^-19.

    “With BBR corrections properly applied, no noise floor is observed and the clocks average below 5 × 10 -19 .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Methods. · p. 11

    Without phase-noise cancellation, the first-order Doppler shift is ≤1 × 10^-16 for Yb-1 and ≤0.5 × 10^-16 for Yb-2.

    “Without cancellation, we evaluate this shift to be ≤1 × 10 -16 for Yb-1 and ≤0.5 × 10 -16 for Yb-2 under the present operating conditions.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Methods. · p. 12

    Without correcting for the BBR shift, the clocks encounter a noise floor of 1 × 10^-18, consistent with ~100 mK deviations.

    “In Fig. 3 it is seen that without correcting for the BBR shift, the clocks encounter a noise floor of 1 × 10 -18 , consistent with the ~100 mK deviations we observe.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § Methods. · p. 11

    Applying this suppression factor, the Doppler shift is no larger than 2 × 10^-20 for Yb-1 and 1 × 10^-20 for Yb-2.

    “Applying this suppression factor to the uncancelled Doppler shift, we assess this shift to be no larger than 2 × 10 -20 for Yb-1 and 1 × 10 -20 for Yb-2.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingcitation
    § Discussion. · p. 8

    The redshift transformation to the reference frame of TT has an uncertainty of 6 × 10^-18, limited by several-centimetre-level state-of-the-art geodetic determination, much larger than the total measurement uncertainty between the clocks.

    “However, the redshift transformation to the reference frame of TT has an uncertainty of 6 × 10 -18 (limited by the several-centimetre-level state-of-the-art geodetic determination), much larger than the total measurement uncertainty between the clocks 32 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [32] Bruinsma, S. L. et al. ESA’s satellite-only gravity field model via the direct approach based on all GOCE data. Geophys. Res. Lett. 41, 7508–7514 (2014). source

      Not checked in the free run.

  • May combine two claims.

    Findingown data
    § Atomic clock performance beyond the geodetic limit · p. 4

    The background gas shift for Yb-1 is -5.5(5) × 10^-18, and for Yb-2, -3.6(3) × 10^-18.

    “The shift for Yb-1 is therefore -5.5(5) × 10 -18 , and for Yb2, -3.6(3) × 10 -18 .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingnone given
    § Methods. · p. 13

    The model uncertainty of the lattice light shift is common-mode between the two clocks and is thus suppressed in the differential uncertainty.

    “We note that the model uncertainty of the lattice light shift is common-mode between the two clocks and is thus suppressed in the differential uncertainty.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § Methods. · p. 15

    The vector Stark shift is uncorrelated, but the second-order Zeeman coefficient uncertainty is common-mode, yielding a differential uncertainty of 1 × 10^-19.

    “The vector Stark shift is uncorrelated, but the coefficient uncertainty is common-mode, yielding a differential uncertainty of 1 × 10 -19 .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § Methods. · p. 17

    Servo error is common-mode between the two clocks due to the shared local oscillator and is suppressed to a high degree.

    “Due to the shared local oscillator, servo error is common-mode between the two clocks, and is suppressed to a high degree.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Methods. · p. 14

    For the sideband-cooled sample, the operational magic wavelength is 394,798,267.7(5) MHz, leading to an experimental lattice light shift uncertainty of 8 × 10^-19.

    “For our sideband-cooled sample, we find an operational magic wavelength of 394,798,267.7(5) MHz, leading to an experimental lattice light shift uncertainty of 8 × 10 -19 .”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Findingnone given
    § Methods. · p. 14

    The enhancement cavity prevents any significant lattice intensity mismatch from occurring on Yb-2.

    “The enhancement cavity prevents any significant lattice intensity mismatch from occurring on Yb-2.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingnone given
    § Methods. · p. 16

    Residual population of clock atoms in the depleted nuclear spin state is suppressed by at least 99.5%, and the π-(σ-) transitions are detuned by ±400 (∓750) Hz.

    “This population is suppressed by at least 99.5 %, and the π - ( σ -) transitions are detuned by ±400 ( ∓ 750) Hz.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Methods. · p. 15

    For 560-ms Rabi spectroscopy, the probe AC Stark shift is 2 × 10^-20, with uncertainty conservatively assessed at 50% of its value.

    “For 560-ms Rabi spectroscopy, the probe shift is found to be 2 × 10 -20 , with uncertainty conservatively assessed at 50 % of its value.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Methods. · p. 18

    The one-second instability is 1.5 × 10^-16, which remains significantly higher than the expected quantum-projection-noise limit (<5 × 10^-17) due to technical sources of noise.

    “We note that the one-second instability of 1.5 × 10 -16 remains significantly higher than the expected quantum-projection-noise limit (< 5 × 10 -17 , for the conditions discussed above), due to technical sources of noise.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingcitation
    § Methods. · p. 17

    The phase transients from the switching AOM are largely random, average to <50 mrad, and are suppressed with a time constant of <20 μs.

    “The switching AOM also serves as the phase-noise-cancellation AOM 42 that, when locked, leads to phase transients that are largely random, averaging to <50 mrad, and are suppressed with a time constant of <20 μs.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [42] Falke, S., Misera, M., Sterr, U. & Lisdat, C. Delivering pulsed and phase stable light to atoms of an optical clock. Appl. Phys. B 107, 301–311 (2012). source

      Not checked in the free run.

  • May combine two claims.

    Findingown data
    § Methods. · p. 18

    The heights of lattice-trapped atoms within Yb-1 and Yb-2 are measured to 2 mm resolution, leading to further shifts of 154.9(2) × 10^-18 and 151.1(2) × 10^-18, respectively.

    “The atomic sample is localised by means of the position of the atomic detection laser, and the heights of the lattice-trapped atoms within Yb-1 and Yb-2 are measured to 2 mm resolution, leading to a further shift of 154.9(2) × 10 -18 and 151.1(2) × 10 -18 , respectively.”
    Quote in the paperSubstantial claim

  • The quote only partly states this claim.

    Findingown data
    § Methods. · p. 14

    The linear Zeeman effect splits the π-transitions by 199.516(2) Hz/G from centre.

    “We find that the linear Zeeman effect splits the -transitions by 199.516(2) Hz/G from centre, in good agreement with a previous measurement 30 .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [30] Zhang, X. et al. Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism. Science 345, 1467–1473 (2014). source

      Not checked in the free run.

  • May combine two claims.

    Findingcitation
    § Methods. · p. 15

    For Yb-2, the vector Stark shift is negligible and the Zeeman uncertainty is 1 × 10^-19, limited by knowledge of the second-order coefficient.

    “For Yb-2, a well-defined linear eigen-polarization is coupled into the build-up cavity, leading to a negligible vector Stark shift 25 and a Zeeman uncertainty of only 1 × 10 -19 , limited by knowledge of the second-order coefficient.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [25] Ushijima, I., Takamoto, M., Das, M., Ohkubo, T. & Katori, H. Cryogenic optical lattice clocks. Nat. Photon. 9, 185–189 (2015). source

      Not checked in the free run.

  • May combine two claims.

    Findingreasoning
    § Methods. · p. 16

    The closest spectroscopic features are transverse sidebands detuned by only 60 Hz from the carrier, but they are highly symmetric and largely suppressed by probing collinear to the lattice laser.

    “The closest spectroscopic features are the transverse sidebands, detuned by only 60 Hz from the carrier. However, they are highly symmetric due to the large number of transverse motional states and are largely suppressed by probing collinear to the lattice laser.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § Methods. · p. 14

    The differential uncertainty of the lattice light shift is only 2 × 10^-19, as the operational magic wavelength suppresses uncertainty due to small differences in trap depth.

    “The differential uncertainty is only 2 × 10 -19 , as the operational magic wavelength suppresses uncertainty due to small differences in trap depth.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning
    § Methods. · p. 15

    For Yb-1, the second-order Zeeman shift is -118.1(2) × 10^-18, with uncertainty limited by knowledge of the residual vector Stark shift.

    “For Yb-1, the second-order Zeeman shift is -118.1(2) × 10 -18 , with an uncertainty limited by knowledge of the residual vector Stark shift.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Methods. · p. 17

    The DDS frequency update technical source of error is consistent with zero at the level of 7 × 10^-20, leading to a differential uncertainty of 1 × 10^-19.

    “By synchronizing a counter to the clock interrogation and directly counting the DDS frequency, we confirm that this technical source of error is consistent with zero at the level of 7 × 10 -20 , leading to a differential uncertainty of 1 × 10 -19”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Competing financial interests. · p. 27

    The background gas collision shift is -5.5 × 10^-18 for Yb-1 and -3.6 × 10^-18 for Yb-2, with differential uncertainty 0.3 × 10^-18.

    “Background gas collisions | -5.5 | 0.5 | -3.6 | 0.3 | 0.3 |”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Findingown data
    § Competing financial interests. · p. 27

    The optical frequency synthesis shift is 0 with uncertainty <0.1 × 10^-18 for both clocks, differential <0.1 × 10^-18.

    “Optical frequency synthesis | 0 | <0.1 | 0 | <0.1 | <0.1 |”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Competing financial interests. · p. 27

    The gravity shift from the TT reference frame is 180,819 × 10^-18 for Yb-1 and 180,815 × 10^-18 for Yb-2, with differential uncertainty 0.3 × 10^-18.

    “Gravity shift from TT reference frame | 180,819 | 6 | 180,815 | 6 | 0.3 |”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Findingown data
    § Competing financial interests. · p. 27

    The total clock uncertainty budget for Yb-1 is -2,486.5 × 10^-18 with uncertainty 1.4, and for Yb-2 is -2,494.7 × 10^-18 with uncertainty 1.4.

    “Total | -2,486.5 | 1.4 | -2,494.7 | 1.4 | |”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Competing financial interests. · p. 27

    The lattice light experimental shift is -1.5 × 10^-18 for both Yb-1 and Yb-2, with differential uncertainty 0.2 × 10^-18.

    “Lattice light (experimental) | -1.5 | 0.8 | -1.5 | 0.8 | 0.2 |”
    Quote in the paperNot a substantial claim

  • May combine two claims. The quote only partly states this claim.

    Findingreasoning
    § Competing financial interests. · p. 27

    The total shift from the TT reference frame is 178,333 × 10^-18 for Yb-1 and 178,320 × 10^-18 for Yb-2, with differential uncertainty 0.8 × 10^-18.

    “Total shift from TT reference frame | 178,333 | 6 | 178,320 | 6 | 0.8 |”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingreasoning
    § Methods. · p. 19

    Inclusion of the excluded eleventh dataset would not significantly change the average frequency difference.

    “We note that, due to the larger error bars associated with it, inclusion of this set would not significantly change the average.”
    Quote in the paperNot a substantial claim

  • May combine two claims. The quote only partly states this claim.

    Findingown data
    § Competing financial interests. · p. 27

    The probe Stark shift is 0.02 × 10^-18 for both clocks, with uncertainty 0.01 and differential <0.01 × 10^-18.

    “Probe Stark | 0.02 | 0.01 | 0.02 | 0.01 | <0.01 |”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingreasoning
    § Methods. · p. 19

    An eleventh dataset, with a noise floor of 7 × 10^-18 at ≥10^4 s, is excluded because of the post-selection criterion.

    “An eleventh dataset, with a noise floor of 7 × 10 -18 at ≥ 10 4 s, is excluded because of the latter criterion.”
    Quote in the paperNot a substantial claim

  • May combine two claims. The quote only partly states this claim.

    Findingown data
    § Competing financial interests. · p. 27

    The second-order Zeeman shift is -118.1 × 10^-18 for Yb-1 and -117.9 × 10^-18 for Yb-2, with differential uncertainty 0.1 × 10^-18.

    “Second-order Zeeman* | -118.1 | 0.2 | -117.9 | 0.1 | 0.1 |”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims. The quote only partly states this claim.

    Findingown data
    § Competing financial interests. · p. 27

    The servo error shift is 0.03 × 10^-18 for both clocks, with uncertainty 0.05 and differential <0.01 × 10^-18.

    “Servo error | 0.03 | 0.05 | 0.03 | 0.05 | <0.01 |”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § Competing financial interests. · p. 27

    The blackbody radiation shift is -2,361.2 × 10^-18 for Yb-1 and -2,371.7 × 10^-18 for Yb-2, with differential uncertainty 0.6 × 10^-18.

    “Blackbody radiation* | -2,361.2 | 0.9 | -2,371.7 | 1.0 | 0.6 |”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Competing financial interests. · p. 27

    The DC Stark shift is consistent with zero with uncertainty <0.07 × 10^-18 for Yb-1 and <0.04 × 10^-18 for Yb-2, differential <0.08 × 10^-18.

    “DC Stark | 0 | <0.07 | 0 | <0.04 | <0.08 |”
    Quote in the paperSubstantial claim

  • May combine two claims. The quote only partly states this claim.

    Findingown data
    § Competing financial interests. · p. 27

    The line pulling shift is 0 with uncertainty <0.1 × 10^-18 for both clocks, differential <0.1 × 10^-18.

    “Line pulling | 0 | <0.1 | 0 | <0.1 | <0.1 |”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims. The quote only partly states this claim.

    Findingown data
    § Competing financial interests. · p. 27

    The tunnelling shift is 0 with uncertainty <0.001 × 10^-18 for both clocks, differential <0.001 × 10^-18.

    “Tunnelling | 0 | <0.001 | 0 | <0.001 | <0.001 |”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Atomic clock performance beyond the geodetic limit · p. 3

    Relative heights between two nearby locations, as much as a few hundred km apart, can be determined with millimetre resolution by spirit levelling.

    “Relative heights between two nearby (as much as a few hundred km) locations can be determined with millimetre resolution by spirit levelling 19”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [19] Vanicek, P., Castle, R. O. & Balazs, E. I. Geodetic leveling and its applications. Rev. Geophys. 18, 505–524 (1980). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data
    § Atomic clock performance beyond the geodetic limit · p. 2

    Near the surface of Earth, clock comparisons at the 1 × 10^-18 level provide 1 cm resolution along gravity, outperforming state-of-the-art geodetic techniques.

    “Near the surface of Earth, clock comparisons at the 1 × 10 -18 level provide 1 cm resolution along gravity, outperforming state-of-the-art geodetic techniques.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Near the surface of Earth, relativistic effects amount to a fractional frequency shift of 1.1 × 10^-18 per cm of vertical displacement.

  • May combine two claims.

    Study design and conductcitation
    § Atomic clock performance beyond the geodetic limit · p. 4

    The thermal shields facilitate characterisation of Stark effects from blackbody radiation and provide an in-situ Faraday enclosure shielding the atoms from static electric fields.

    “This facilitates characterisation of a key systematic effect afflicting optical clocks, Stark effects from blackbody radiation bathing the ultracold atoms, and further provides an insitu Faraday enclosure shielding the atoms from static electric fields due to stray charges on the vacuum apparatus 24 .”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [23] Beloy, K. et al. Faraday-shielded dc Stark-shift-free optical lattice clock. Phys. Rev. Lett. 120, 183201 (2018). source

      Not checked in the free run.

    • cites [24] Brown, R. C. et al. Hyperpolarizability and operational magic wavelength in an optical lattice clock. Phys. Rev. Lett. 119, 253001 (2017). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Atomic clock performance beyond the geodetic limit · p. 3

    These clocks are based on optical transitions, in which greater oscillation frequency leads to an increase of 10^5 in the quality factor of the transition and concomitant performance improvements.

    “These clocks are based on optical transitions, in which greater oscillation frequency leads to an increase of 10 5 in the quality factor of the transition and concomitant performance improvements 22 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [22] Beloy, K. et al. Atomic clock with 1 × 10−18 room-temperature blackbody Stark uncertainty. Phys. Rev. Lett. 113, 260801 (2014). source

      Not checked in the free run.

  • May combine two claims.

    Study design and conductcitation
    § Atomic clock performance beyond the geodetic limit · p. 4

    The clocks utilize a one-dimensional optical lattice operating near the magic wavelength, where lowest-order trap light shifts on the clock transition are cancelled, and higher-order lattice effects have been experimentally characterised.

    “These clocks also utilize a one-dimensional optical lattice operating near the magic wavelength, where lowest-order trap light shifts on the clock transition are cancelled, and higher-order lattice effects have been experimentally characterised 25 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [25] Ushijima, I., Takamoto, M., Das, M., Ohkubo, T. & Katori, H. Cryogenic optical lattice clocks. Nat. Photon. 9, 185–189 (2015). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Interpretationcitation
    § Atomic clock performance beyond the geodetic limit · p. 2

    These optical clocks can be used to explore geophysical phenomena, detect gravitational waves, test general relativity and search for dark matter.

    “These optical clocks can further be used to explore geophysical phenomena 10 , detect gravitational waves 11 , test general relativity 12 and search for dark matter 13-17 .”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [10] Bondarescu, R. et al. Ground-based optical atomic clocks as a tool to monitor vertical surface motion. Geophys. J. Int. 202, 1770–1774 (2015). source

      Not checked in the free run.

    • cites [11] Kolkowitz, S. et al. Gravitational wave detection with optical lattice atomic clocks. Phys. Rev. D 94, 124043 (2016). source

      Not checked in the free run.

    • cites [12] Delva, P. et al. Test of special relativity using a fiber network of optical clocks. Phys. Rev. Lett. 118, 221102 (2017). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation
    § Discussion. · p. 8

    Height uncertainty at or below 1 cm, corresponding to fractional frequency uncertainties below 1 × 10^-18, remains at best an optimistic goal.

    “Refinements of geoid models using satellite-based long-wavelength data 33 and terrestrial short-wavelength data 34 may reduce future geoid model uncertainty to a degree, but height uncertainty at or below 1 cm (fractional frequency uncertainties below 1 × 10 -18 ) remains at best an optimistic goal 21,32 .”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [21] Denker, H. et al. Geodetic methods to determine the relativistic redshift at the level of 10−18 in the context of international timescales: a review and practical results. J. Geod. 92, 487–516 (2018). source

      Not checked in the free run.

    • cites [32] Bruinsma, S. L. et al. ESA’s satellite-only gravity field model via the direct approach based on all GOCE data. Geophys. Res. Lett. 41, 7508–7514 (2014). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Study design and conductnone given
    § Methods. · p. 9

    The atoms are spin-polarized to >99.5% purity on the 556 nm transition.

    “The atoms are spin-polarized to >99.5 % purity on the 556 nm transition.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given
    § Atomic clock performance beyond the geodetic limit · p. 7

    Frequency comparisons are performed with a blinding protocol that prevents the operator from having knowledge of the frequency difference during individual measurements.

    “The frequency comparisons are performed with a blinding protocol (see Methods) that prevents the operator from having knowledge of the frequency difference during individual measurements.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductown data
    § Atomic clock performance beyond the geodetic limit · p. 7

    The results are the culmination of ten blinded measurements, taken over the course of more than a month.

    “The results reported here are the culmination of ten blinded measurements, taken over the course of more than a month.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Study design and conductnone given
    § Methods. · p. 9

    An atomic shutter blocks the atomic beam during spectroscopy, preventing collisional shifts from the atomic beam as well as excess blackbody radiation shifts from the hot oven.

    “An atomic shutter blocks the atomic beam during spectroscopy, preventing collisional shifts from the atomic beam as well as excess blackbody radiation shifts from the hot oven.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationown data
    § Atomic clock performance beyond the geodetic limit · p. 7

    Experimentally investigating reproducibility is indispensable for substantiating an uncertainty budget.

    “This experience underscores the indispensability of experimentally investigating reproducibility for substantiating an uncertainty budget.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationcitation
    § Discussion. · p. 8

    With optical clock performance at the levels demonstrated here, these clocks now enable beyond-state-of-the-art geodetic measurements and fundamental physics studies.

    “With optical clock performance at the levels demonstrated here, these clocks now enable beyond-stateof-the-art geodetic measurements and fundamental physics studies 7,8,10,13,15 .”
    Quote in the paperSubstantial claim0 of 5 sources checked
    • cites [7] Delva, P. & Lodewyck, J. Atomic clocks: new prospects in metrology and geodesy. Acta Futura 7, 67–78 (2013).

      Not checked in the free run.

    • cites [8] Lion, G. et al. Determination of a high spatial resolution geopotential model using atomic clock comparisons. J. Geod. 91, 597–611 (2017). source

      Not checked in the free run.

    • cites [10] Bondarescu, R. et al. Ground-based optical atomic clocks as a tool to monitor vertical surface motion. Geophys. J. Int. 202, 1770–1774 (2015). source

      Not checked in the free run.

    • cites [13] Derevianko, A. & Pospelov, M. Hunting for topological dark matter with atomic clocks. Nat. Phys. 10, 933–936 (2014). source

      Not checked in the free run.

    • cites [15] Wcisło, P. et al. Experimental constraint on dark matter detection with optical atomic clocks. Nat. Astron. 1, 0009 (2016). source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Study design and conductnone given
    § Methods. · p. 19

    A post-selection criterion is established that data averages as white frequency noise for averaging times greater than 100 s.

    “A post-selection criterion, that data averages as white frequency noise for averaging times greater than 100 s, is also established.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § Methods. · p. 15

    Stray DC electric fields have been observed to cause Stark shifts on the order of 10^-13 for some optical lattice clocks.

    “Stray DC electric fields have been observed to cause Stark shifts on the order of 10 -13 for some optical lattice clocks 48 .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [48] Lee, W. D., Shirley, J. H., Walls, F. L. & Drullinger, R. E. Systematic errors in cesium beam frequency standards introduced by digital control of the microwave excitation. Proc. IEEE Int. Freq. Control Symp. Expo. 113–117 (1995). source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Study design and conductreasoning
    § Methods. · p. 19

    The operator is completely blind to the frequency difference until the termination of the measurement.

    “The operator is completely blind to the frequency difference until the termination of the measurement.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductreasoning
    § Methods. · p. 19

    A blinding protocol adds a large offset to the frequency difference observed by the operator, pseudorandomly chosen from a uniform distribution spanning ±1 kHz, many orders of magnitude greater than the sub-millihertz resolution.

    “To eliminate this source of bias, we employ a blinding protocol that adds a large offset to the frequency difference observed by the operator. This offset is pseudorandomly chosen from a uniform distribution spanning ±1 kHz, many orders of magnitude greater than the sub-millihertz resolution of the experiment.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductnone given
    § Methods. · p. 19

    Prior to each blinded measurement, both clocks are assessed to verify full compliance with the uncertainty budget of Table 1.

    “Prior to commencing each blinded measurement, both clocks are comprehensively assessed to verify that they are fully compliant with the uncertainty budget of Table 1.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductnone given
    § Methods. · p. 19

    The assessment includes verifying via motional sideband spectroscopy that the trap depth is within 10% of 50 Er and the longitudinal temperature is lower than 1 μK.

    “For instance, the operator verifies via motional sideband spectroscopy that the trap depth is within 10 % of 50 Er and that the longitudinal temperature is lower than 1 μK.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § Methods. · p. 18

    Synchronous interrogation does not reject other sources of error, and reaching low instability at long timescales requires control of all systematic shifts.

    “Despite rejecting the Dick effect, synchronous interrogation does not reject other sources of error, and reaching low instability at long timescales requires control of all systematic shifts.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisenone given
    § Methods. · p. 16

    The presence of other spectroscopic features near the atomic transition can lead to an apparent shift of the line.

    “The presence of other spectroscopic features near the atomic transition can lead to an apparent shift of the line.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § Methods. · p. 18

    A clock elevated above the geoid experiences a gravitational blueshift, as well as a redshift due to increasing centrifugal acceleration.

    “A clock that is elevated above the geoid experiences a gravitational blueshift, as well as a redshift due to increasing centrifugal acceleration 51 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [51] Takamoto, M., Takano, T. & Katori, H. Frequency comparison of optical lattice clocks beyond the Dick limit. Nat. Photon. 5, 288–292 (2011). source

      Not checked in the free run.

  • May combine two claims.

    Study design and conductown data
    § Methods. · p. 17

    Servo error is controlled by probing the transition first in ascending frequency order followed by descending frequency order, cancelling cavity drift at <500 μHz/s by digital feedforward correction and implementing a second integrator.

    “We control servo error by probing our transition first in ascending frequency order followed by descending frequency order, cancelling cavity drift at <500 μHz/s by digital feedforward correction and implementing a second integrator.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductnone given
    § Methods. · p. 19

    Statistical error bars are assigned by applying a 1/√ fit to the total Allan deviation assuming a servo attack time of 20 s and extrapolating to the full measurement time.

    “Statistical error bars are assigned by applying a 1/ √ fit to the total Allan deviation assuming a servo attack time of 20 s and extrapolating to the full measurement time.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given
    § Methods. · p. 18

    As dictated by relativity, measurements of time in different reference frames should be transformed into a shared reference system.

    “As dictated by relativity, measurements of time in different reference frames should be transformed into a shared reference system.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given
    § Methods. · p. 16

    σ± transitions result from driving the ΔmF = ±1 transition.

    “σ± -transitions result from driving the Δ m F = ±1 transition.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Premisenone given
    § Methods. · p. 19

    For frequency comparisons such as those reported in Fig. 4, it would be possible for the operator to stop the experiment when statistical fluctuations temporarily push the average frequency difference to zero.

    “For example, for frequency comparisons such as those reported in Fig. 4 it would be possible for the operator to stop the experiment when statistical fluctuations temporarily push the average frequency difference to zero.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisenone given
    § Methods. · p. 17

    Clock operation requires pulsing the 578 nm interrogation laser with an acousto-optic modulator, a process known to induce phase chirps.

    “Clock operation requires pulsing the 578 nm interrogation laser with an acousto-optic modulator, a process which is known to induce phase chirps.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given
    § Methods. · p. 19

    The assessment consists of a checklist of all parameters that can change from day to day.

    “This assessment consists of a checklist of all parameters that can change from day to day.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

    Premisenone given
    § Methods. · p. 19

    Operator bias can be an important source of error in any physical measurement.

    “Operator bias can be an important source of error in any physical measurement.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Premisenone given
    § Methods. · p. 16

    In a horizontal lattice, tunnelling of atoms between lattice sites could potentially result in a shift as large as the bandwidth of the Bloch state.

    “In a horizontal lattice, tunnelling of atoms between lattice sites could potentially result in a shift as large as the bandwidth of the Bloch state.”
    Quote in the paperSubstantial claim
71 of 71

  • The paper relies on this without support.

    The theory of relativity correctly prescribes that the passage of time is not absolute but impacted by an observer's reference frame.

    “However, the theory of relativity prescribes that the passage of time is not absolute, but impacted by an observer's reference frame.”

  • The paper relies on this without support.

    Near the surface of Earth, relativistic effects amount to a fractional frequency shift of 1.1 × 10^-18 per cm of vertical displacement.

    “Near the surface of Earth, relativistic effects amount to a fractional frequency shift of 1.1 × 10 -18 per cm of vertical displacement.”
2 of 2

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Present-day optical clocks and frequency links have already demonstrated geopotential (height) comparisons at the few-centimetre level.

    “Present-day optical clocks and frequency links have already demonstrated geopotential (height) comparisons at the few-centimetre level [7, 14, 27]”

    From Chapter 1 Theoretical background (1996) · cites this paper as [14]

    The paper reports optical-clock comparisons with precision sufficient for centimetre-scale height resolution (Atomic clock performance beyond the geodetic limit, pp. 2, 7). But the clocks compared were closely located; the Discussion (p. 8) treats long-baseline comparisons as hypothetical and attributes the several-centimetre geodetic determination to existing height measurements. It does not report a demonstrated few-centimetre geopotential comparison using an optical-clock frequency link. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • Optical atomic clocks with uncertainty and accuracy around 1 × 10 -18 and even higher have been developed in various laboratories.

    “However, with the fast development of high-precision clock manufacturing technology in recent years, optical atomic clocks (OACs), which have uncertainty and accuracy level of around 1 × 10 -18 and even higher have been developed in various laboratories [17][18][19][20].”

    From Unification of a Global Height System at the Centimeter-Level Using Precise Clock Frequency Signal Links (2023) · cites this paper as [17]

  • Simulation experiments show that the precision of the geopotential difference between two ground sites determined by the satellite frequency signal transmission method is about 2 to 5 cm in height under the assumption that the accuracy of optical atomic clocks is about 1 × 10 -18.

    “Simulation experiments show that the precision of the geopotential difference between two ground sites determined by the SFST method is about 2∼5 cm in height [34], under the assumption that the accuracy of the OACs is about 1 × 10 -18 , which is achievable currently [17][18][19].”

    From Unification of a Global Height System at the Centimeter-Level Using Precise Clock Frequency Signal Links (2023) · cites this paper as [17]

Cites

Flagged first, then by citations

Research works printed but not linked: 2

  1. Delva, P. & Lodewyck, J. Atomic clocks: new prospects in metrology and geodesy. Acta Futura 7, 67–78 (2013).
  2. Hofmann-Wellenhof, B. & Moritz, H. Physical Geodesy (Springer, Vienna, 2005).

Cited by

Sorted by citations

Related

Authors
McGrew, W. F., Zhang, X., Fasano, R. J., Schäffer, S. A., Beloy, K., Nicolodi, D., Brown, R. C., Hinkley, N., Milani, G., Schioppo, M., Yoon, T. H., & Ludlow, A. D.
Affiliations
  • National Institute of Standards and Technology (US)
  • University of Copenhagen (DK)
Corresponding author
Ludlow, A. D.
ORCID
Venue
Nature
Publisher
Springer Science and Business Media LLC
Published
2018-11-28
Volume
564
Issue
7734
Pages
87-90
ISSN
  • 0028-0836 (ISSN-L)
  • 1476-4687
DOI
10.1038/s41586-018-0738-2
OpenAlex
W2902127691
Semantic Scholar
4c50666e42d4875a16275612f249482ad58e5dee
Cited by
727
References
48
Citations by year
2026: 60 · 2025: 97 · 2024: 112 · 2023: 113 · 2022: 81 · 2021: 83 · 2020: 103 · 2019: 75 · 2018: 3
FWCI
30.53
Type
journal article
Language
en
Open access
Licence
www.springer.com/tdm (tdm)
Locations
  • Nature (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • Figshare (submittedVersion, public-domain)
  • Research at the University of Copenhagen (University of Copenhagen) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Frequency and Time Standards
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
  • Physical Sciences › Computer Science › Computer Networks and Communications › Network Time Synchronization Technologies
Keywords
optical atomic clocks, systematic uncertainties, measurement instability, reproducibility, geopotential, geodesy, gravitational potential, tests of general relativity, gravitational waves, dark matter searches

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-10.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-10.

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