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

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Chou, C. W., Hume, D. B., Koelemeij, J. C. J., Wineland, D. J. & Rosenband, T. Frequency comparison of two high-accuracy Al+ optical clocks. Phys. Rev. Lett. 104, 070802 (2010).

    CAS  ADS  Article  Google Scholar 

  2. 2.

    Nicholson, T. L. et al. Systematic evaluation of an atomic clock at 2×10−18 total uncertainty. Nat. Commun. 6, 6896 (2015).

    CAS  ADS  Article  Google Scholar 

  3. 3.

    Huntemann, N., Sanner, C., Lipphardt, B., Tamm, C. & Peik, E. Single-ion atomic clock with 3×10−18 systematic uncertainty. Phys. Rev. Lett. 116, 063001 (2016).

    CAS  ADS  Article  Google Scholar 

  4. 4.

    Schioppo, M. et al. Ultra-stable optical clock with two cold-atom ensembles. Nat. Photon. 11, 48–52 (2017).

    CAS  ADS  Article  Google Scholar 

  5. 5.

    Takano, T. et al. Geopotential measurements with synchronously linked optical lattice clocks. Nat. Photon. 10, 662–666 (2016).

    CAS  ADS  Article  Google Scholar 

  6. 6.

    Chou, C. W., Hume, D. B., Rosenband, T. & Wineland, D. J. Optical clocks and relativity. Science 329, 1630–1633 (2010).

    CAS  ADS  Article  Google Scholar 

  7. 7.

    Delva, P. & Lodewyck, J. Atomic clocks: new prospects in metrology and geodesy. Acta Futura 7, 67–78 (2013).

    Google Scholar 

  8. 8.

    Lion, G. et al. Determination of a high spatial resolution geopotential model using atomic clock comparisons. J. Geod. 91, 597–611 (2017).

    ADS  Article  Google Scholar 

  9. 9.

    Grotti, J. et al. Geodesy and metrology with a transportable optical clock. Nat. Phys. 14, 437–441 (2018).

    CAS  Article  Google Scholar 

  10. 10.

    Bondarescu, R. et al. Ground-based optical atomic clocks as a tool to monitor vertical surface motion. Geophys. J. Int. 202, 1770–1774 (2015).

    ADS  Article  Google Scholar 

  11. 11.

    Kolkowitz, S. et al. Gravitational wave detection with optical lattice atomic clocks. Phys. Rev. D 94, 124043 (2016).

    ADS  Article  Google Scholar 

  12. 12.

    Delva, P. et al. Test of special relativity using a fiber network of optical clocks. Phys. Rev. Lett. 118, 221102 (2017).

    CAS  ADS  Article  Google Scholar 

  13. 13.

    Derevianko, A. & Pospelov, M. Hunting for topological dark matter with atomic clocks. Nat. Phys. 10, 933–936 (2014).

    CAS  Article  Google Scholar 

  14. 14.

    Arvanitaki, A., Huang, J. & Van Tilburg, K. Searching for dilaton dark matter with atomic clocks. Phys. Rev. D 91, 015015 (2015).

    ADS  Article  Google Scholar 

  15. 15.

    Wcisło, P. et al. Experimental constraint on dark matter detection with optical atomic clocks. Nat. Astron. 1, 0009 (2016).

    Article  Google Scholar 

  16. 16.

    Hees, A., Guéna, J., Abgrall, M., Bize, S. & Wolf, P. Searching for an oscillating massive scalar field as a dark matter candidate using atomic hyperfine frequency comparisons. Phys. Rev. Lett. 117, 061301 (2016).

    CAS  ADS  Article  Google Scholar 

  17. 17.

    Roberts, B. M. et al. Search for domain wall dark matter with atomic clocks on board global positioning system satellites. Nat. Commun. 8, 1195 (2017).

    ADS  Article  Google Scholar 

  18. 18.

    Soffel, M. et al. The IAU 2000 resolutions for astrometry, celestial mechanics, and metrology in the relativistic framework: explanatory supplement. Astron. J. 126, 2687–2706 (2003).

    ADS  Article  Google Scholar 

  19. 19.

    Vanicek, P., Castle, R. O. & Balazs, E. I. Geodetic leveling and its applications. Rev. Geophys. 18, 505–524 (1980).

    ADS  Article  Google Scholar 

  20. 20.

    Wang, Y. M., Saleh, J., Li, X. & Roman, D. R. The US Gravimetric Geoid of 2009 (USGG2009): model development and evaluation. J. Geod. 86, 165–180 (2012).

    ADS  Article  Google Scholar 

  21. 21.

    Denker, H. et al. Geodetic methods to determine the relativistic redshift at the level of 10−18 in the context of international timescales: a review and practical results. J. Geod. 92, 487–516 (2018).

    ADS  Article  Google Scholar 

  22. 22.

    Beloy, K. et al. Atomic clock with 1 × 10−18 room-temperature blackbody Stark uncertainty. Phys. Rev. Lett. 113, 260801 (2014).

    CAS  ADS  Article  Google Scholar 

  23. 23.

    Beloy, K. et al. Faraday-shielded dc Stark-shift-free optical lattice clock. Phys. Rev. Lett. 120, 183201 (2018).

    CAS  ADS  Article  Google Scholar 

  24. 24.

    Brown, R. C. et al. Hyperpolarizability and operational magic wavelength in an optical lattice clock. Phys. Rev. Lett. 119, 253001 (2017).

    CAS  ADS  Article  Google Scholar 

  25. 25.

    Ushijima, I., Takamoto, M., Das, M., Ohkubo, T. & Katori, H. Cryogenic optical lattice clocks. Nat. Photon. 9, 185–189 (2015).

    CAS  ADS  Article  Google Scholar 

  26. 26.

    Akatsuka, T., Takamoto, M. & Katori, K. Optical lattice clocks with non-interacting bosons and fermions. Nat. Phys. 4, 954–959 (2008).

    CAS  Article  Google Scholar 

  27. 27.

    Campbell, S. L. et al. A Fermi-degenerate three-dimensional optical lattice clock. Science 358, 90–94 (2017).

    CAS  ADS  Article  Google Scholar 

  28. 28.

    Gibble, K. Scattering of cold-atom coherences by hot atoms: frequency shifts from background-gas collisions. Phys. Rev. Lett. 110, 180802 (2013).

    ADS  Article  Google Scholar 

  29. 29.

    Lemke, N. D. et al. Spin-1/2 optical lattice clock. Phys. Rev. Lett. 103, 063001 (2009).

    CAS  ADS  Article  Google Scholar 

  30. 30.

    Zhang, X. et al. Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism. Science 345, 1467–1473 (2014).

    CAS  ADS  Article  Google Scholar 

  31. 31.

    Pavlis, N. K. & Weiss, M. A. A re-evaluation of the relativistic redshift on frequency standards at NIST, Boulder, Colorado, USA. Metrologia 54, 535–548 (2017).

    ADS  Article  Google Scholar 

  32. 32.

    Bruinsma, S. L. et al. ESA’s satellite-only gravity field model via the direct approach based on all GOCE data. Geophys. Res. Lett. 41, 7508–7514 (2014).

    ADS  Article  Google Scholar 

  33. 33.

    Smith, D. The GRAV-D Project: Gravity for the Redefinition of the American Vertical Datum (NOAA, 2007).

  34. 34.

    Curtis, E. A., Oates, C. W. & Hollberg, L. Quenched narrow-line second- and third-stage laser cooling of 40Ca. J. Opt. Soc. Am. B 20, 977–984 (2003).

    CAS  ADS  Article  Google Scholar 

  35. 35.

    Nemitz, N. et al. Frequency ratio of Yb and Sr clocks with 5×10−17 uncertainty at 150 seconds averaging time. Nat. Photon. 10, 258–261 (2016).

    CAS  ADS  Article  Google Scholar 

  36. 36.

    Lemke, N. D. et al. p-wave cold collisions in an optical lattice clock. Phys. Rev. Lett. 107, 103902 (2011).

    CAS  ADS  Article  Google Scholar 

  37. 37.

    Julienne, P. S. & Mies, F. H. Collisions of ultracold trapped atoms. J. Opt. Soc. Am. B 6, 2257–2269 (1989).

    CAS  ADS  Article  Google Scholar 

  38. 38.

    Dzuba, V. A. & Derevianko, A. Dynamic polarizabilities and related properties of clock states of the ytterbium atom. J. Phys. B 43, 074011 (2010).

    ADS  Article  Google Scholar 

  39. 39.

    Swallows, M. D. et al. Suppression of collisional shifts in a strongly interacting lattice clock. Science 331, 1043–1046 (2011).

    CAS  ADS  Article  Google Scholar 

  40. 40.

    Katori, H., Takamoto, M., Pal’chikov, V. G. & Ovsiannikov, V. D. Ultrastable optical clock with neutral atoms in an engineered light shift trap. Phys. Rev. Lett. 91, 173005 (2003).

    ADS  Article  Google Scholar 

  41. 41.

    Ma, L., Jungner, P., Ye, J. & Hall, J. L. Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by an optical fiber or other time-varying path. Opt. Lett. 19, 1777–1779 (1994).

    CAS  ADS  Article  Google Scholar 

  42. 42.

    Falke, S., Misera, M., Sterr, U. & Lisdat, C. Delivering pulsed and phase stable light to atoms of an optical clock. Appl. Phys. B 107, 301–311 (2012).

    CAS  ADS  Article  Google Scholar 

  43. 43.

    Porsev, S. G. & Derevianko, A. Multipolar theory of blackbody radiation shift of atomic energy levels and its implications for optical lattice clocks. Phys. Rev. A 74, 020502 (2006).

    ADS  Article  Google Scholar 

  44. 44.

    Katori, H., Ovsiannikov, V. D., Marmo, S. I. & Palchikov, V. G. Strategies for reducing the light shift in atomic clocks. Phys. Rev. A 91, 052503 (2015).

    ADS  Article  Google Scholar 

  45. 45.

    Boyd, M. et al. Nuclear spin effects in optical lattice clocks. Phys. Rev. A 76, 022510 (2007).

    ADS  Article  Google Scholar 

  46. 46.

    Lodewyck, J., Zawada, M., Lorini, L., Gurov, M. & Lemonde, P. Observation and cancellation of a perturbing dc Stark shift in strontium optical lattice clocks. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 411–415 (2012).

    Article  Google Scholar 

  47. 47.

    Lemonde, P. & Wolf, P. Optical lattice clock with atoms confined in a shallow trap. Phys. Rev. A 72, 033409 (2005).

    ADS  Article  Google Scholar 

  48. 48.

    Lee, W. D., Shirley, J. H., Walls, F. L. & Drullinger, R. E. Systematic errors in cesium beam frequency standards introduced by digital control of the microwave excitation. Proc. IEEE Int. Freq. Control Symp. Expo. 113–117 (1995).

  49. 49.

    Hofmann-Wellenhof, B. & Moritz, H. Physical Geodesy (Springer, Vienna, 2005).

    Google Scholar 

  50. 50.

    Bize, S. et al. Interrogation oscillator noise rejection in the comparison of atomic fountains. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1253–1255 (2000).

    CAS  Article  Google Scholar 

  51. 51.

    Takamoto, M., Takano, T. & Katori, H. Frequency comparison of optical lattice clocks beyond the Dick limit. Nat. Photon. 5, 288–292 (2011).

    CAS  ADS  Article  Google Scholar 

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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.

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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.

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Correspondence to A. D. Ludlow.

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McGrew, W.F., Zhang, X., Fasano, R.J. et al. Atomic clock performance enabling geodesy below the centimetre level. Nature 564, 87–90 (2018).

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  • Optical Lattice Clock
  • Clock Laser
  • Differential Uncertainty
  • Collisional Shift
  • Lateral Laser

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