International optical clock comparison using the European optical fiber network

Phys. Rev. Res. 8, 033250 (2026) · DOI: 10.1103/l4bh-ryxs · arXiv: 2604.27963

License: CC BY 4.0.

Abstract

Optical clocks have achieved remarkable estimated fractional frequency uncertainties reaching the $10^{-18}$ level and below, enabling applications in fundamental physics, general relativity, and geodesy. However, the challenge of verifying the international consistency of optical clocks remains critical as efforts intensify toward redefining the SI second based on an optical transition or transitions. We report on a two-month international clock comparison campaign involving seven optical clocks in four national metrology institutes (INRIM, LNE-OP, NPL, and PTB) connected via the optical fiber network established in Europe. The campaign resulted in optical frequency ratios with uncertainties ranging from $7.7\times10^{-18}$ to $6.1\times10^{-17}$. Among the results, the $^{171}$Yb$^+$(E3) clocks at NPL and PTB demonstrated agreement within an uncertainty of $7.7\times10^{-18}$, marking the first international verification of two independently developed optical clocks below one part in $10^{17}$. The operation of the $^{199}$Hg clock at LNE-OP (formerly LNE-SYRTE) resulted in frequency ratios with improved uncertainties with $^{171}$Yb$^+$(E3), $^{171}$Yb, and $^{87}$Sr optical clocks. These results provide input for the redefinition of the second and underscore how fiber-linked clock networks can advance metrology and scientific applications.

Figures

39 panels with data across 6 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

Illustrative figure, no extractable data. Shown in the paper PDF.

Fig. 2

The underlying data is not available. The figure is shown in the paper PDF.

Fig. 3

• panel (1): Daily averages of the SYRTE-Hg/NPL-E3Yb+3 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty, orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (2): Daily averages of the SYRTE-Hg/PTB-Yb1E3 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty, orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (3): Daily averages of the SYRTE-Hg/IT-Yb1 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty, orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (4): Daily averages of the SYRTE-Hg/NPL-Sr1 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty, orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (5): Daily averages of the SYRTE-Hg/PTB-Sr3 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty (without the PTB-Sr3 systematic uncertainty), orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (6): Daily averages of the PTB-Yb1E2/PTB-Yb1E3 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty, orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (7): Daily averages of the NPL-E3Yb+3/PTB-Yb1E3 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty, orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (8): Daily averages of the NPL-E3Yb+3/IT-Yb1 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty, orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (9): Daily averages of the NPL-E3Yb+3/NPL-Sr1 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty, orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (10): Daily averages of the NPL-E3Yb+3/PTB-Sr3 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty (without the PTB-Sr3 systematic uncertainty), orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (11): Daily averages of the PTB-Yb1E3/IT-Yb1 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty, orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (12): Daily averages of the PTB-Yb1E3/NPL-Sr1 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty, orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (13): Daily averages of the PTB-Yb1E3/PTB-Sr3 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty (without the PTB-Sr3 systematic uncertainty), orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (14): Daily averages of the IT-Yb1/NPL-Sr1 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty, orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (15): Daily averages of the IT-Yb1/PTB-Sr3 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty (without the PTB-Sr3 systematic uncertainty), orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv
• panel (16): Daily averages of the NPL-Sr1/PTB-Sr3 ratio as the fractional offset $y = R/R_0 - 1$, in units of $10^{-18}$, against MJD. Blue error bars are the total uncertainty (without the PTB-Sr3 systematic uncertainty), orange ones the statistical uncertainty. Two light blue lines bound the average with its total uncertainty, the printed shaded band; the printed box with $B$, $n$ and $T$ is not drawn. data.csv

Fig. 4

• panel (1): Allan deviation (ADEV) of the SYRTE-Hg/NPL-E3Yb+3 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (2): Allan deviation (ADEV) of the SYRTE-Hg/PTB-Yb1E3 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (3): Allan deviation (ADEV) of the SYRTE-Hg/IT-Yb1 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (4): Allan deviation (ADEV) of the SYRTE-Hg/NPL-Sr1 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (5): Allan deviation (ADEV) of the SYRTE-Hg/PTB-Sr3 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (6): Allan deviation (ADEV) of the PTB-Yb1E2/PTB-Yb1E3 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (7): Allan deviation (ADEV) of the NPL-E3Yb+3/PTB-Yb1E3 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (8): Allan deviation (ADEV) of the NPL-E3Yb+3/IT-Yb1 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (9): Allan deviation (ADEV) of the NPL-E3Yb+3/NPL-Sr1 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (10): Allan deviation (ADEV) of the NPL-E3Yb+3/PTB-Sr3 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (11): Allan deviation (ADEV) of the PTB-Yb1E3/IT-Yb1 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (12): Allan deviation (ADEV) of the PTB-Yb1E3/NPL-Sr1 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (13): Allan deviation (ADEV) of the PTB-Yb1E3/PTB-Sr3 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (14): Allan deviation (ADEV) of the IT-Yb1/NPL-Sr1 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (15): Allan deviation (ADEV) of the IT-Yb1/PTB-Sr3 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv
• panel (16): Allan deviation (ADEV) of the NPL-Sr1/PTB-Sr3 frequency ratio against averaging time $\tau$ / s, log-log, with $1\sigma$ error bars assuming white frequency noise. The blue line is the white-frequency-noise fit, scaling as $\tau^{-1/2}$, its value at 1 s in the legend; the green star is the statistical uncertainty at the total measurement time, inflated by the Birge ratio if greater than 1. data.csv

Fig. 5

• panel (1): Correlation coefficient $r$ between the eleven frequency-ratio measurements of Table II, one row and one column per ratio, on a colour scale from $-1$ to 1. data.csv

Fig. 6

• panel (1): Frequency ratio $^{171}\mathrm{Yb}^{+}$(E3)/$^{87}$Sr as the fractional offset $y$ ($10^{-16}$) for each measurement, labelled by institutes and year: this campaign (orange squares) and previous measurements (blue circles), with error bars. The two dotted lines are the uncertainty of the reference ratio, a gray bar in print. The printed chart lists the measurements down the vertical axis. data.csv

Fig. 7

• panel (1): Frequency ratio $^{199}$Hg/$^{171}\mathrm{Yb}^{+}$(E3) as the fractional offset $y$ ($10^{-16}$) for each measurement, labelled by institutes and year: this campaign (orange squares) and previous measurements (blue circles), with error bars. The two dotted lines are the uncertainty of the reference ratio, a gray bar in print. The printed chart lists the measurements down the vertical axis. data.csv
• panel (2): Frequency ratio $^{199}$Hg/$^{171}$Yb as the fractional offset $y$ ($10^{-16}$) for each measurement, labelled by institutes and year: this campaign (orange squares) and previous measurements (blue circles), with error bars. The two dotted lines are the uncertainty of the reference ratio, a gray bar in print. The printed chart lists the measurements down the vertical axis. data.csv
• panel (3): Frequency ratio $^{199}$Hg/$^{87}$Sr as the fractional offset $y$ ($10^{-16}$) for each measurement, labelled by institutes and year: this campaign (orange squares) and previous measurements (blue circles), with error bars. The two dotted lines are the uncertainty of the reference ratio, a gray bar in print. The printed chart lists the measurements down the vertical axis. data.csv

Fig. 8

• panel (1): Frequency ratio $^{171}\mathrm{Yb}^{+}$(E3)/$^{171}$Yb as the fractional offset $y$ ($10^{-16}$) for each measurement, labelled by institutes and year: this campaign (orange squares) and previous measurements (blue circles), with error bars. The two dotted lines are the uncertainty of the reference ratio, a gray bar in print. The printed chart lists the measurements down the vertical axis. data.csv
• panel (2): Frequency ratio $^{171}$Yb/$^{87}$Sr as the fractional offset $y$ ($10^{-16}$) for each measurement, labelled by institutes and year: this campaign (orange squares) and previous measurements (blue circles), with error bars. The two dotted lines are the uncertainty of the reference ratio, a gray bar in print. The printed chart lists the measurements down the vertical axis. data.csv

Cite

Marco Pizzocaro et al. (44 authors). International optical clock comparison using the European optical fiber network. Phys. Rev. Res. 8, 033250 (2026). https://doi.org/10.1103/l4bh-ryxs

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