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Determination of the relativistic redshift of atomic clocks at the level of 10-18


The frequency instability and systematic uncertainty of the latest generation of optical atomic clocks is now approaching the one part in 1018 level. Comparisons between clocks must account for the relativistic redshift of the clock frequencies, which is proportional to the corresponding gravity (gravitational plus centrifugal) potential of the clocks. For contributions to international timescales, the relativistic redshift correction must be applied with respect to a conventional zero potential value, which is derived from the mean sea level or geoid.

To benefit fully from the uncertainty of the optical clocks, the gravity potential must be determined with an accuracy of 0.1 m2/s2, equivalent to 0.01 m vertical height. Two geodetic approaches were investigated in a European research project [1]: geometric levelling and the Global Navigation Satellite Systems (GNSS)/geoid approach. Geometric levelling gives potential differences corresponding to millimetre uncertainty over shorter distances (several kilometres), but is susceptible to systematic errors at the decimetre level over large distances. The GNSS/geoid approach gives absolute gravity potential values, but with an uncertainty corresponding to about 2 cm in vertical height. For large distances, the GNSS/geoid approach should therefore be better than geometric levelling. The research activities enable the comparison of atomic clocks at the metrology institutes INRiM (Turin), LNE-SYRTE (Paris), NPL (London) and PTB (Braunschweig) with an uncertainty of the relativistic redshift of 2×10−18.


[1] H. Denker, L. Timmen, C. Voigt, S. Weyers, E. Peik, H. S. Margolis, P. Delva, P. Wolf, G. Petit, Geodetic methods to determine the relativistic redshift at the level of 10-18 in the context of international timescales: a review and practical results, Journal of Geodesy 92 (5), 487-516 (2018)