Absolute Frequency of 87Sr at 1.8×10-16 Uncertainty by Tracing NICT-Sr1 to Remote Primary Frequency Standards

Abstract

The optical lattice clock NICT-Sr1 [1] regularly reports calibration data for the international atomic time TAI, obtained by intermittent measurements of a flywheel hydrogen maser. Continuous frequency measurements of this maser against the local UTC(NICT) and a GNSS satellite link then provide a traceable chain to UTC, which differs from TAI by the number of accumulated leap seconds, but shares its frequency. By using data publicly available from the International Bureau of Weights and Measures (BIPM), we extend the chain to eight individual primary frequency standards that reported calibration data for suitably similar intervals. For 63 such directly traced comparisons, we individually determine nine uncertainty contributions, including clock statistical and systematic uncertainties, the satellite link instability, and operating interval extrapolations that address measurement deadtime and mismatched evaluation periods. A covariance matrix constructed from these contributions addresses correlated and uncorrelated uncertainties. A suitable distribution of weights is found by a least-squares approach based on the Gauss-Markov theorem. Direct tracing to individual primary standards allows a flexible choice of evaluation intervals and provides results in terms of the nominal SI second even when the BIPM calculation of the TAI scale interval error includes contributions of secondary standards. From 776 hours of strontium clock data acquired over four years, we thus find the absolute frequency of the 87Sr clock transition to be f(Sr) = 429 228 004 229 873.08(8) Hz [2], with a fractional uncertainty of less than 1.8e-16, approaching the systematic limits of the best realizations of the SI second. The evaluation shows no statistical anomalies or significant variation over time. Our result is consistent with a recent measurement performed at PTB [3] against local primary standards, which determined the 87Sr clock transition frequency as f(Sr@PTB) = 429 228 004 229 873.00(7) Hz. A loop closure over the absolute frequencies of 87Sr, 171Yb [4,5] and direct optical measurements of their ratio [6] also finds excellent consistency. If this level of agreement between independent measurements is reflected in a revision of the recommended frequencies provided by the International Committee of Weights and Measures (CIPM), it will support optical lattice clocks operating as frequency standards with absolute uncertainties of 2e-16 or below, outperforming all but the best cesium clocks even before a redefinition of the SI second.