Yb/Sr optical clock comparison at 2.2E-18 uncertainty over a 1350-km fiber link

Lei Hou; Xiang-Pei Liu; Zhuan-Xian Xiong; Fa-Xi Chen; Wen-Xuan Song; Jian-Yu Guan; Qiang Zhu; Yu-Chen Zhang; Xiang Zhang; Bing Wang; De-Zhi Xiong; De-Quan Kong; Jia-Hao Zhang; Long-Fei Liao; Shao-Mao Wang; Xing-Yang Cui; Ping Xu; Peng Liu; Jie Li; Xiao Jiang; Ling-Xiang He; Li-Bo Li; Qi Shen; Youchao Xie; Lei Wang; Sheng-Kai Liao; Juan Yin; Cheng-Zhi Peng; Wen-Bin Shen; Bao-Long Lu; Han-Ning Dai; Yu-Ao Chen; Qiang Zhang; Hai-Feng Jiang; Jian-Wei Pan

AI summary · arXiv: 2610.34250v1 · physics.optics

Yb/Sr optical clock comparison at 2.2E-18 uncertainty over a 1350-km fiber link

Lei Hou, Xiang-Pei Liu, Zhuan-Xian Xiong, Fa-Xi Chen, Wen-Xuan Song, Jian-Yu Guan, Qiang Zhu, Yu-Chen Zhang,

and 27 more authors

Xiang Zhang, Bing Wang, De-Zhi Xiong, De-Quan Kong, Jia-Hao Zhang, Long-Fei Liao, Shao-Mao Wang, Xing-Yang Cui, Ping Xu, Peng Liu, Jie Li, Xiao Jiang, Ling-Xiang He, Li-Bo Li, Qi Shen, Youchao Xie, Lei Wang, Sheng-Kai Liao, Juan Yin, Cheng-Zhi Peng, Wen-Bin Shen, Bao-Long Lu, Han-Ning Dai, Yu-Ao Chen, Qiang Zhang, Hai-Feng Jiang, Jian-Wei Pan

Original paper Submitted to arXiv on 25 Oct. 2026 License: NONEXCLUSIVE-DISTRIB 1.0

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The essentials

A 1,350-km fiber comparison of Wuhan Yb and Shanghai Sr clocks determined their frequency ratio with 2.18×10⁻¹⁸ total uncertainty and detected a tidal signal.

Question

Can different optical clocks in separate cities be compared over a long-distance link with uncertainty below 5×10⁻¹⁸, as required for validating clock evaluations? Can the same comparison detect time-varying gravitational potential from Earth tides?

Method

The authors linked a ytterbium lattice clock in Wuhan and a strontium lattice clock in Shanghai using a phase-stabilized 1,350-km fiber network. Across 58 days, they collected 274 effective hours in 16 jump-free segments, combined segment ratios with a random-effect model, and assessed tidal response against a template based on DE421 ephemerides and the FES2022 ocean-tide model.

Findings

Result The measured Yb/Sr frequency ratio was 1.2075070393433377160, with total standard uncertainty 2.18×10⁻¹⁸.
See the passage in the paper
Combining these components in quadrature gives the total standard uncertainty $2.18\times 10^{-18}$; the reported ratio is therefore
Authors’ interpretation The ratio comparison reached the uncertainty level required by the redefinition roadmap for comparisons between different transitions in different laboratories.
See the passage in the paper
To our knowledge, this is the first intercity long distance frequency-ratio measurement whose total uncertainty reaches the level required by the redefinition roadmap.
Result The measured beat showed a tidal-template response amplitude of 0.87(15), differing from zero by 5.7 standard deviations and consistent with the expected response of +1.
See the passage in the paper
The within-segment correlation against a template built from the DE421 ephemerides 33 and the FES2022 ocean-tide model 34 is positive in 12 out of 16 segments, and the precision-weighted response amplitude is $0.87\,(15)$ ($1\sigma$), which differs from zero at $5.7\sigma$ and agrees with the expected response of $+1$ within the statistical uncertainty.
Authors’ interpretation The comparison demonstrates that an intercity optical-clock link can measure time-varying gravitational potential at the 10⁻¹⁸ level.
See the passage in the paper
Clock comparisons over large baselines directly sense the time-variable gravitational potential, providing an independent means of testing and calibrating tide and loading models at the $10^{-18}$ level, where the limits of the current model seen here can be refined, or removed, by more comparison data from an expanding optical-clock network.

Limitations

The reported ratio does not eliminate uncertainty in the clock systematic evaluations; the discrepancy with the NIST–JILA measurement remains unresolved.
See the passage in the paper
The remaining disagreement with the NIST–JILA determination keeps the accuracy budgets of the participating clocks open questions, which the redefinition of the second requires to be closed.
The tide model is not equally reliable for all components: the correction degrades the record in the ocean-loading band, identifying that model component as weaker.
See the passage in the paper
In the diurnal and semi-diurnal ocean-loading band it degrades it, indicating that the ocean-loading model is the weaker part.

Why it matters

The result extends clock-ratio comparisons at the required uncertainty from local measurements to an intercity link, supporting validation of optical-clock evaluations. The authors argue that expanding such networks can also improve gravity and tide models and enable wide-area clock comparisons.

Written by AI from the paper. Passages are checked word for word against the text we analysed; the rest may contain errors.

AI-generated keywords: optical lattice clocks; frequency-ratio measurement; fibre link; gravitational redshift; tidal effects

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Comprehensive Summary
Layman's Summary
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Original abstract

The paper compares a ytterbium optical lattice clock in Wuhan with a strontium optical lattice clock in Shanghai. The central question is whether different types of clocks in separate cities, connected over a long distance, can measure a frequency ratio precisely enough to help validate uncertainty evaluations relevant to a future redefinition of the SI second. The authors also investigate whether the comparison can detect changes in Earth’s gravitational potential caused by tides. The clocks were connected by a phase-stabilized telecom-fibre link with a route length of 1,350 kilometres. The link used a commercial network and 21 relay stations. Optical frequency combs at both ends connected each clock transition to the transmitted carrier. Over 58 days, the experiment collected 274 hours of synchronous data in 16 accepted, jump-free segments across three campaigns. The team estimated a ratio for each segment, assessed its statistical uncertainty using the final available point of the overlapping Allan deviation, and combined the segments using several statistical methods, including a Bayesian random-effects model. They excluded a seventeenth segment because experimental settings were still being adjusted. A separate levelling campaign measured the static geopotential difference between the clock locations. The authors also calculated a time-varying tidal signal using solid-Earth tide and ocean-loading models. The reported ytterbium-to-strontium frequency ratio is 1.2075070393433377160, with a total standard uncertainty of 2.18 × 10⁻¹⁸. The statistical contribution is 1.14 × 10⁻¹⁸. The stated clock-systematic contributions are 0.92 × 10⁻¹⁸ for strontium and 1.3 × 10⁻¹⁸ for ytterbium. The uncertainty from the static geopotential correction is 0.946 × 10⁻¹⁸, while the fibre link and frequency comb each contribute less than 0.1 × 10⁻¹⁸. The measured static geopotential difference is 280.042 ± 0.085 square metres per second. The combined statistical result remains stable across three estimators and when individual segments are removed. The comparison also reveals a tidal signature. During the campaign, the predicted time-varying redshift reached a diurnal amplitude of about 6 × 10⁻¹⁸. Although no individual segment resolved the signal on its own, the combined fitted response was 0.87 ± 0.15 times the model prediction. This corresponds to a 5.7-standard-deviation detection and is consistent with the expected response of one. The model-based correction shifted the reported ratio by 1.9 × 10⁻¹⁹. The authors interpret this finding as evidence that clock comparisons over this baseline can detect changes in gravitational potential and help test geophysical tide models. The result meets the stated 5 × 10⁻¹⁸ uncertainty target for comparisons relevant to redefining the second and, according to the authors, is the first intercity measurement at this level. However, it does not establish that all clock uncertainty evaluations are correct. The measured value differs from the NIST–JILA result by −5.78 × 10⁻¹⁸ relative to that measurement, exceeding the two results’ combined standard uncertainty. The authors identify clock-systematic evaluations as the likeliest remaining source of disagreement and call for independent follow-up measurements. They also caution that the result relies on a limited set of accepted segments and a model-based tidal correction. In particular, the ocean-loading component of the model performs less successfully than the solid-Earth tide component.

Two Optical Clocks, 1,350 Kilometres Apart

How precisely can two different kinds of optical clocks agree when they are in separate cities? That question matters beyond clockmaking: comparisons between independent clocks can help test the uncertainty evaluations that would underpin a future redefinition of the SI second. In “Yb/Sr optical clock comparison at 2.2E-18 uncertainty over a 1350-km fiber link,” Lei Hou, Xiang-Pei Liu, Zhuan-Xian Xiong, Fa-Xi Chen, Wen-Xuan Song, Jian-Yu Guan et al. report a long-distance comparison between an ytterbium clock in Wuhan and a strontium clock in Shanghai.

The experiment reached a total standard uncertainty of 2.18 × 10⁻¹⁸, meeting the authors’ stated 5 × 10⁻¹⁸ target for comparisons relevant to redefining the second. The team also found a clear signature of the changing gravitational potential caused by tides. Together, these results demonstrate what remote optical-clock comparisons can measure—and where important uncertainties remain.

Connecting the Clocks

The clocks were linked by a phase-stabilized telecom-fibre system following a 1,350-kilometre route through a commercial network. The connection used 21 relay stations. Optical frequency combs at both ends linked each clock’s transition to the carrier transmitted through the fibre, enabling the researchers to compare the frequencies while correcting for fluctuations in the link.

Over 58 days, the team collected 274 hours of synchronous measurements. These were divided into 16 accepted, jump-free segments across three campaigns. A seventeenth segment was left out because experimental settings were still being adjusted. For each accepted segment, the researchers estimated the ytterbium-to-strontium frequency ratio and assessed statistical uncertainty using the final available point of the overlapping Allan deviation.

Rather than rely on a single way of combining the data, they used several statistical approaches, including a Bayesian random-effects model. The resulting statistical estimate remained stable across three estimators and when individual segments were removed. That consistency supports the robustness of the combined result, although the total measurement still rests on a limited set of accepted segments.

A Precise Ratio—and Its Uncertainty

The reported ytterbium-to-strontium frequency ratio is 1.2075070393433377160. Its total standard uncertainty is 2.18 × 10⁻¹⁸, including both statistical and systematic contributions. The statistical uncertainty is 1.14 × 10⁻¹⁸. The stated clock-systematic contributions are 0.92 × 10⁻¹⁸ for strontium and 1.3 × 10⁻¹⁸ for ytterbium.

Because clocks at different heights experience different gravitational potentials, comparing them also requires a correction for their locations. A separate levelling campaign measured the static geopotential difference between Wuhan and Shanghai as 280.042 ± 0.085 square metres per second. The associated uncertainty contributes 0.946 × 10⁻¹⁸ to the ratio’s uncertainty. By contrast, the fibre link and the frequency combs each contribute less than 0.1 × 10⁻¹⁸.

Reaching the target is an important step, but it does not prove that every clock uncertainty evaluation is correct. The measured ratio differs from the NIST–JILA result by −5.78 × 10⁻¹⁸ relative to that measurement, a difference larger than the two results’ combined standard uncertainty. The authors identify clock-systematic evaluations as the likeliest remaining source of disagreement and call for independent follow-up measurements.

Detecting the Tides

Earth’s gravitational potential changes as tides move mass in the solid Earth and oceans. The researchers calculated the expected time-varying signal using solid-Earth tide and ocean-loading models. During the campaign, the predicted diurnal redshift reached an amplitude of about 6 × 10⁻¹⁸.

No individual data segment resolved the tidal signal on its own. But when the segments were combined, the fitted response was 0.87 ± 0.15 times the model prediction. That amounts to a 5.7-standard-deviation detection and is consistent with the expected response of one. Applying the model-based correction shifted the reported frequency ratio by 1.9 × 10⁻¹⁹.

The detection suggests that clock comparisons over this baseline can track changes in gravitational potential and help test geophysical tide models. The authors note a qualification: the ocean-loading component of the model performed less successfully than the solid-Earth tide component. The tidal correction is therefore model-based, and its interpretation deserves continued scrutiny.

What the Result Shows—and What Comes Next

The authors describe this as the first intercity measurement at this uncertainty level. It shows that different optical-clock species, separated by a long distance, can be compared precisely enough to meet a stated target relevant to a future redefinition of the second. It also demonstrates that a long-baseline clock link can reveal a geophysical signal too small to resolve in any one segment.

The result is not the final word on optical-clock accuracy. The discrepancy with the NIST–JILA measurement, the limited number of accepted segments and the reliance on a tidal model all point to the need for further independent comparisons. As more clocks and links are brought into such tests, researchers will be better able to distinguish clock-systematic errors from link, statistical and geophysical effects—and to determine how confidently optical clocks can support the next definition of time.

Created on 02 Nov. 2026

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Weekly letter Presented in "Physics of matter and light this week" of 2 November 2026. Physics of matter and light this week: Hidden order, from atomic bonds to distant clocks

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Yb/Sr optical clock comparison at 2.2E-18 uncertainty over a 1350-km fiber link

The essentials

Question

Method

Findings

Limitations

Why it matters

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Definitions

Two Optical Clocks, 1,350 Kilometres Apart

Connecting the Clocks

A Precise Ratio—and Its Uncertainty

Detecting the Tides

What the Result Shows—and What Comes Next

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