Atomic clock frequency ratios with fractional uncertainty $\leq 3.2 \times 10^{-18}$

TL;DR

This work reports ultra-precise frequency ratios between three optical clocks based on ${}^{27}\mathrm{Al}^{+}$, ${}^{171}\mathrm{Yb}$, and ${}^{87}\mathrm{Sr}$ with total fractional uncertainties below $3.2\times 10^{-18}$, marking a key milestone toward redefining the SI second. A common ultrastable reference delivered over a 3.6 km fiber link and a cryogenic Si cavity underpin the improved stability, enabling rapid, high-precision comparisons and enhanced sensitivity to non-white noise processes. A hierarchical Bayesian framework, complemented by alternative analysis approaches, yields robust ratio estimates and reveals cross-clock correlations and between-day variability, while detailed systematic and network analyses underscore both the progress and remaining challenges for interlaboratory consensus. The results advance optical clock metrology, inform redefinition thresholds, and highlight the need for repeated, cross-lab measurements to reconcile remaining discrepancies.

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 (19)

• Figure 1: Simplified schematic of the Boulder optical clock network. Two independent oscillators---a cyrogenic silicon (Si) optical cavity and a hydrogen maser for the radio-frequency---are distributed across multiple laboratories via the 3.6 km-long Boulder Research and Administration Network (BRAN) optical fiber link. The ${}^{27}\text{Al}^{+}$ and ${}^{171}\text{Yb}$ clocks are located at NIST, and the ${}^{87}\text{Sr}$ clock is located at JILA. Local ULE cavity-referenced lasers in all laboratories are steered by a common 1542 nm laser locked to the Si cavity at JILA. Frequency combs at JILA and NIST transfer the Si cavity's stability to the clock wavelengths. A stable microwave signal from a maser at NIST is distributed optically to JILA.
• Figure 2: Frequency ratio measurement results. (a) Fractional instability of the ratio measurements. The points are the overlapping Allan deviation of each fractional ratio, calculated for different averaging times $\tau$ and using concatenated data from a single measurement day. The solid lines are a white-frequency-noise model fit to points with $\tau$ greater than the servo attack time of $\sim100$s (color filled points). We extrapolate this fit to the total measurement time (the end of the fitted line) to obtain the statistical uncertainty. The gray diamonds are an upper bound on the instability of the fiber link, estimated by a loopback measurement. (b) Daily ratio measurements are shown as fractional deviations from the final reported values (Eqs. \ref{['eq:ratios']}). The error bars represent statistical uncertainty obtained by the procedure described in (a). The colored shaded regions show the final fractional uncertainties including systematic uncertainties and are $2.2\times 10^{-18}$, $3.2\times 10^{-18}$, and $3.1\times 10^{-18}$ for $\text{Al}^{+}/\text{Sr}$, $\text{Al}^{+}/\text{Yb}$, and $\text{Yb}/\text{Sr}$ ratios, respectively. All uncertainties represent the 68 % confidence interval.
• Figure 3: (a) Reported frequency ratio measurements with direct links NemitzYbSrRatio2016LindvallClockComparisons2025bacon2021. Only the five lowest uncertainty results are shown for $\text{Yb}/\text{Sr}$. The solid lines with shaded regions are the CIPM 2021 recommended values and their 1-$\sigma$ uncertainties. An expanded version is presented in End Matter Fig. \ref{['fig:ratiohistoricaldataexpanded']}. (b) Schematic of the end-to-end loopback test for evaluating frequency network accuracy and stability. PLL: optical phase-locked loop. The acousto-optic modulators (AOMs) and optical phase-locked loops (PLLs) use frequencies referenced to the maser, and are indicated for each path.
• Figure 4: Insights making use of three clocks running simultaneously. (a) Correlations between day-to-day fractional variation in pairs of frequency ratios (y vs x). Each data point is one measurement day, restricted to times when all three clocks operated simultaneously. The mean of all nine days is subtracted from each data point. The $\text{Al}^{+}/\text{Yb}$ and $\text{Al}^{+}/\text{Sr}$ ratios are strongly correlated, as their fluctuations are dominated by single-ion quantum projection noise. The $\text{Yb}/\text{Sr}$ ratio shows no statistically significant correlation with either of the ratios involving ${}^{27}\text{Al}^{+}$. Red lines and shaded areas are a linear fit to the data and 1-$\sigma$ uncertainty, with slope given by $1.08(18)$, $-0.55(76)$, and $0.95(97)$ for the three subplots. (b) Estimating the fractional frequency stability of the three individual clocks. Points show overlapping Allan deviations for each clock, calculated using a three-cornered hat analysis. Solid lines are weighted white noise model fits to data points with averaging time $\tau> 100~\unit{s}$ (filled markers).
• Figure 5: Evolution of frequency ratio measurements. Asterisks (*) indicate the values we presented in BACON21 bacon2021akamatsuFrequencyRatioMeasurement2014campbellAbsoluteFrequencyThe87Sr2008grebingRealizationTimescaleAccurate2016grottiGeodesyMetrologyTransportable2018hachisuSItraceableMeasurementOptical2017akimImprovedAbsoluteFrequency2017alemkeSpin122009lodewyckOpticalMicrowaveClock2016mcgrewOpticalSecondVerifying2019NemitzYbSrRatio2016pizzocaroAbsoluteFrequencyMeasurement2017rosenbandFrequencyRatioAl+and2008takamotoFrequencyRatiosSr2015. The errorbars represent 1-$\sigma$ uncertainty. Direct ratio measurements performed after CIPM 2017 are shown, organized by measurement method and year fujiedaAdvancedSatelliteBasedFrequency2018hisaiImprovedFrequencyRatio2021pizzocaroIntercontinentalComparisonOptical2021LindvallClockComparisons2025. Colored lines and shaded regions represent the mean values and uncertainties from CIPM 2021 margolisCIPMListRecommended2024, while gray lines and shaded regions indicate the mean ratio and uncertainty from CIPM 2017 riehleCIPMListRecommended2018a. Marker styles denote different measurement methods: filled circles for direct optical measurements, open circles for absolute frequency measurements, and gray-filled circles for microwave measurements.