Fiber Network Verifies Independent Optical Clocks Below 10⁻¹⁷

Optical clocks now estimate fractional-frequency uncertainties at, and sometimes below, $10^{-18}$, but their agreement across independently built systems remains a practical test for a future optical definition of the second. The authors report a 2023 campaign that connected seven clocks at INRIM, LNE-OP, NPL, and PTB through European optical-fiber links. Its central result is an international comparison of the NPL and PTB $^{171}\mathrm{Yb}^+(\mathrm{E3})$ ion clocks with $7.7\times10^{-18}$ uncertainty: the first such check of independently developed optical clocks below one part in $10^{17}$.

Core Contribution

The contribution is a network-scale consistency measurement rather than a new clock architecture. By operating multiple species and clock types in one linked campaign, the study turns pairwise frequency-ratio measurements into a test of whether national standards agree at the level needed for international metrology. The campaign also supplies new direct ratios involving the $^{199}\mathrm{Hg}$ lattice clock at LNE-OP, whose earlier comparison history included discrepancies without a definitive experimental cause.

That scope matters because a prospective redefinition of the SI second cannot rest only on uncertainty budgets reported by individual laboratories. It needs comparisons that expose mismatches between independent realizations. The paper's value is therefore both the smallest reported cross-border uncertainty and a more realistic account of where the network still finds tension.

Technical Approach

The campaign ran for two months in early 2023, using stabilized optical-fiber links to compare clocks in four European national metrology institutes. The network included $^{171}\mathrm{Yb}^+(\mathrm{E3})$ ion clocks at NPL and PTB, a $^{199}\mathrm{Hg}$ clock at LNE-OP, and $^{171}\mathrm{Yb}$ and $^{87}\mathrm{Sr}$ lattice-clock measurements involving the participating institutes. Fiber transfer is intended to make the link contribution negligible relative to the clock comparisons, allowing the measured ratios to probe the clocks rather than satellite-transfer noise.

The paper expresses each ratio as a fractional offset, $y=R/R_0-1$, relative to a reference ratio from a least-squares adjustment of standard frequencies. Daily averages combine statistical and systematic uncertainty in quadrature. The reported uncertainty bands account for excess scatter by inflating the statistical component with the Birge ratio when it exceeds one; the Allan-deviation analysis tests the assumed white-frequency-noise scaling with averaging time. Correlations between ratio measurements are also evaluated, an important detail when several ratios share clocks and links.

Results and Analysis

The strongest evidence comes from the NPL–PTB $^{171}\mathrm{Yb}^+(\mathrm{E3})$ comparison, which agrees within $7.7\times10^{-18}$. Across the campaign, reported ratio uncertainties span $7.7\times10^{-18}$ to $6.1\times10^{-17}$. These are direct experimental measurements over a shared campaign, not extrapolations from separate clock evaluations.

Figure 3 presents the daily ratio offsets, their statistical and total error bars, and the measurement duration and Birge ratio for each comparison. This presentation makes a useful distinction: the nominal precision of a daily point is not automatically the uncertainty of the campaign average when repeatability shows extra scatter.

For $^{199}\mathrm{Hg}$, the LNE-OP-to-NPL $^{199}\mathrm{Hg}/^{87}\mathrm{Sr}$ ratio is consistent within $2\sigma$ with two earlier measurements and with the reference ratio. The authors attribute greater confidence relative to earlier campaigns to a longer campaign and revised treatment of systematic effects including quadratic Zeeman, cold-collision, and background-gas collision shifts. The result strengthens the mercury clock's comparison record, but does not prove that every historical discrepancy has been explained.

The paper is appropriately less tidy for $^{171}\mathrm{Yb}/^{87}\mathrm{Sr}$. One INRIM–NPL result disagrees by $4\sigma$ with a 2018 NIST–JILA measurement and an earlier ROCIT 2022 result, while agreeing with RIKEN measurements and a more recent BACON result. The authors report no identified experimental error or overlooked systematic effect. That unresolved conflict is not peripheral: it is evidence that network comparisons are still needed before ratio data can be treated as fully settled inputs to a redefined second.

Limits in Practice

This is a strong campaign measurement, but it covers seven clocks, four institutes, and a two-month window rather than a global, continuous ensemble. The uncertain source of several ratio inconsistencies also constrains the interpretation. The paper establishes that fiber-linked international verification can reach the low-$10^{-18}$ range for one key pair; it does not establish universal agreement among optical-clock species or laboratories.