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Atomic clock performance enabling geodesy below the centimetre level


The passage of time is tracked by counting oscillations of a frequency reference, such as Earth’s revolutions or swings of a pendulum. By referencing atomic transitions, frequency (and thus time) can be measured more precisely than any other physical quantity, with the current generation of optical atomic clocks reporting fractional performance below the 10−17 level1,2,3,4,5. However, the theory of relativity prescribes that the passage of time is not absolute, but is affected by an observer’s reference frame. Consequently, clock measurements exhibit sensitivity to relative velocity, acceleration and gravity potential. Here we demonstrate local optical clock measurements that surpass the current ability to account for the gravitational distortion of space-time across the surface of Earth. In two independent ytterbium optical lattice clocks, we demonstrate unprecedented values of three fundamental benchmarks of clock performance. In units of the clock frequency, we report systematic uncertainty of 1.4 × 10−18, measurement instability of 3.2 × 10−19 and reproducibility characterized by ten blinded frequency comparisons, yielding a frequency difference of [−7 ± (5)stat ± (8)sys] × 10−19, where ‘stat’ and ‘sys’ indicate statistical and systematic uncertainty, respectively. Although sensitivity to differences in gravity potential could degrade the performance of the clocks as terrestrial standards of time, this same sensitivity can be used as a very sensitive probe of geopotential5,6,7,8,9. Near the surface of Earth, clock comparisons at the 1 × 10−18 level provide a resolution of one centimetre along the direction of gravity, so the performance of these clocks should enable geodesy beyond the state-of-the-art level. These optical clocks could further be used to explore geophysical phenomena10, detect gravitational waves11, test general relativity12 and search for dark matter13,14,15,16,17.

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We acknowledge financial support from the National Institute of Standards and Technology, the NASA Fundamental Physics programme, the Defense Advanced Research Projects Agency (DARPA) Quantum Assisted Sensing and Readout (QuASAR) programme and PECASE. R.C.B. acknowledges support from the National Research Council Research Associateship programme. A.D.L. acknowledges support from the International Space Science Institute for contributions to the Spacetime Metrology, Clocks and Relativistic Geodesy Workshop. We also thank T. Fortier and H. Leopardi for femtosecond optical frequency comb measurements, and J. Kitching and D. Hume for careful reading of this manuscript.

Reviewer information

Nature thanks K. Bongs, P. Delva and T. Ido for their contribution to the peer review of this work.

Author information

W.F.M., X.Z., R.J.F., S.A.S., D.N. and A.D.L. carried out the instability and reproducibility measurements. W.F.M., X.Z., S.A.S., K.B., D.N., R.C.B., N.H., G.M., M.S., T.H.Y. and A.D.L. contributed to the evaluation of the uncertainty budget. A.D.L. supervised this work. All authors contributed to the final manuscript. Contributions to this article by workers at NIST, an agency of the US Government, are not subject to US copyright.

Competing interests

The authors declare no competing interests.

Correspondence to A. D. Ludlow.

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Further reading

Fig. 1: Simplified experimental scheme.
Fig. 2: Sources of systematic uncertainty.
Fig. 3: Measurement instability.
Fig. 4: Characterization of reproducibility.


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