Least-squares analysis of clock frequency comparison data to deduce optimized frequency and frequency ratio values

Abstract

A method is presented for analysing over-determined sets of clock frequency comparison data involving standards based on a number of different reference transitions. This least-squares adjustment procedure, which is based on the method used by CODATA to derive a self-consistent set of values for the fundamental physical constants, can be used to derive optimized values for the frequency ratios of all possible pairs of reference transitions. It is demonstrated to reproduce the frequency values recommended by the International Committee for Weights and Measures, when using the same input data used to derive those values. The effects of including more recently published data in the evaluation is discussed and the importance of accounting for correlations between the input data is emphasised.

12 pages, 4 figures

References in corpus (6)

• Systematic evaluation of an atomic clock at 2e-18 total uncertainty
• Frequency ratio of two optical clock transitions in ${}^{171}$Yb${}^{+}$ and constraints on the time-variation of fundamental constants
• Improved limit on a temporal variation of $m_p/m_e$ from comparisons of Yb${}^{+}$ and Cs atomic clocks
• Progress in Atomic Fountains at LNE-SYRTE
• Direct comparison of a Ca+ single ion clock against a Sr optical lattice clock
• Frequency ratio measurement of 171Yb and 87Sr optical lattice clocks

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