Nils Nemitz, Hidekazu Hachisu, Tadahiro Gotoh, Fumimaru Nakagawa, Hiroyuki Ito, Yuko Hanado, and Tetsuya Ido, National Institute of Information and Communications Technology, Japan

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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. References: [1] H. Hachisu et al. “SI-traceable measurement of an optical frequency at the low 10?16 level without a local primary standard“, Opt. Express 25 8511–23 (2017) DOI: 10.1364/OE.25.008511 [2] N. Nemitz et al. “Absolute frequency of 87Sr at 1.8 × 10?16 uncertainty by reference to remote primary frequency standards”, submitted to Metrologia arXiv:2008.00723 (2020); [3] R. Schwarz et al. “Long term measurement of the 87Sr clock frequency at the limit of primary Cs clocks”, Phys. Rev. Res. 2, 033242 (2020) DOI: 10.1103/PhysRevResearch.2.033242 [4] W. F. McGrew et al. “Towards the optical second: verifying optical clocks at the SI limit”, Optica 6 448-454 (2019) DOI: 10.1364/OPTICA.6.000448 [5] M. Pizzocaro et al. “Absolute frequency measurement of the 1S0–3P0 transition of 171Yb with a link to international atomic time”, Metrologia 57 035007 (2020) DOI: 10.1088/1681-7575/ab50e8 [6] Boulder Atomic Clock Optical Network, “Frequency ratio measurements with 18-digit accuracy using a network of optical clocks“ arXiv: 2005.14694 (2020)