Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Demonstration of 4.8 × 10−17 stability at 1 s for two independent optical clocks


Optical atomic clocks require local oscillators with exceptional optical coherence owing to the challenge of performing spectroscopy on their ultranarrow-linewidth clock transitions. Advances in laser stabilization have thus enabled rapid progress in clock precision. A new class of ultrastable lasers based on cryogenic silicon reference cavities has recently demonstrated the longest optical coherence times to date. Here we utilize such a local oscillator with two strontium (Sr) optical lattice clocks to achieve an advance in clock stability. Through an anti-synchronous comparison, the fractional instability of both clocks is assessed to be \(4.8 \times 10^{ - 17}/\sqrt \tau\) for an averaging time τ (in seconds). Synchronous interrogation enables each clock to average at a rate of \(3.5 \times 10^{ - 17}/\sqrt \tau\), dominated by quantum projection noise, and reach an instability of 6.6 × 10−19 over an hour-long measurement. The ability to resolve sub-10−18-level frequency shifts in such short timescales will affect a wide range of applications for clocks in quantum sensing and fundamental physics.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Experimental layout.
Fig. 2: Laser stability characterization.
Fig. 3: Impact of laser and magnetic field noise on clock instability.
Fig. 4: Spectral purity transfer of the local oscillator.
Fig. 5: Stability comparison between 1D and 3D clocks.

Data availability

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


  1. Bloom, B. J. et al. An optical lattice clock with accuracy and stability at the 10−18 level. Nature 506, 71–75 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Brewer, S. M. et al. 27Al+ quantum-logic clock with a systematic uncertainty below 10−18. Phys. Rev. Lett. 123, 033201 (2019).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Riehle, F. Towards a redefinition of the second based on optical atomic clocks. C. R. Phys. 16, 506–515 (2015).

    Article  Google Scholar 

  8. Huntemann, N. et al. Improved limit on a temporal variation of m p/m e from comparisons of Yb+ and Cs atomic clocks. Phys. Rev. Lett. 113, 210802 (2014).

    Article  ADS  Google Scholar 

  9. Godun, R. M. et al. Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants. Phys. Rev. Lett. 113, 210801 (2014).

    Article  ADS  Google Scholar 

  10. Rosenband, T. et al. Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place. Science 319, 1808–1812 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  13. Sanner, C. et al. Optical clock comparison test of Lorentz symmetry. Nature 567, 204–208 (2019).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. Itano, W. M. et al. Quantum projection noise: population fluctuations in two-level systems. Phys. Rev. A 47, 3554–3570 (1993).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Nicholson, T. L. et al. Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s. Phys. Rev. Lett. 109, 230801 (2012).

    Article  ADS  Google Scholar 

  21. Al-Masoudi, A., Dörscher, S., Häfner, S., Sterr, U. & Lisdat, C. Noise and instability of an optical lattice clock. Phys. Rev. A 92, 063814 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. Kolkowitz, S. et al. Spin–orbit-coupled fermions in an optical lattice clock. Nature 542, 66–70 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. Martin, M. J. et al. A quantum many-body spin system in an optical lattice clock. Science 341, 632–636 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  26. Bishof, M., Zhang, X., Martin, M. J. & Ye, J. Optical spectrum analyzer with quantum-limited noise floor. Phys. Rev. Lett. 111, 093604 (2013).

    Article  ADS  Google Scholar 

  27. Häfner, S. et al. 8 × 10−17 fractional laser frequency instability with a long room-temperature cavity. Opt. Lett. 40, 2112–2115 (2015).

    Article  ADS  Google Scholar 

  28. Kessler, T. et al. A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity. Nat. Photon. 6, 687–692 (2012).

    Article  ADS  Google Scholar 

  29. Matei, D. G. et al. 1.5 μm lasers with sub-10 mHz linewidth. Phys. Rev. Lett. 118, 263202 (2017).

    Article  ADS  Google Scholar 

  30. Zhang, W. et al. Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K. Phys. Rev. Lett. 119, 243601 (2017).

    Article  ADS  Google Scholar 

  31. Robinson, J. M. et al. Crystaline optical cavity at 4 K with thermal noise limited instability and ultralow drift. Optica 6, 240–243 (2019).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. Rubiola, E. & Vernotte, F. The cross-spectrum experimental method. Preprint at (2010).

  34. Dick, J. G. Local oscillator induced instabilities in trapped ion frequency standards. In Proceedings of the 19th Annual Precise Time and Time Interval Meeting, 133–147 (US Naval Observatory, 1988);

  35. Santarelli, G. et al. Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 887 (1998).

    Article  Google Scholar 

  36. Bothwell, T. et al. JILA Sr1 optical lattice clock with uncertainty of 2.0 × 10−18. Preprint at (2019).

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  39. Riehle, F. Optical clock networks. Nat. Photon. 11, 25–31 (2017).

    Article  ADS  Google Scholar 

  40. Cole, G. D., Zhang, W., Martin, M. J., Ye, J. & Aspelmeyer, M. Tenfold reduction of Brownian noise in high-reflectivity optical coatings. Nat. Photon. 7, 644–650 (2013).

    Article  ADS  Google Scholar 

  41. Hutson, R. B., Goban, A., Marti, G. E. & Ye, J. Engineering quantum states of matter for atomic clocks in shallow optical lattices. Preprint at (2019).

  42. Marti, G. E. et al. Imaging optical frequencies with 100 μHz precision and 1.1 μm resolution. Phys. Rev. Lett. 120, 103201 (2018).

    Article  ADS  Google Scholar 

  43. Zhang, W. et al. Reduction of residual amplitude modulation to 1 × 10−6 for frequency modulation and laser stabilization. Opt. Lett. 39, 1980–1983 (2014).

    Article  ADS  Google Scholar 

  44. Milner, W. R. et al. Demonstration of a time scale based on a stable optical carrier. Preprint at (2019).

  45. Hänsel, W. et al. All polarization-maintaining fiber laser architecture for robust femtosecond pulse generation. Appl. Phys. B 123, 41 (2017).

    Article  ADS  Google Scholar 

  46. Hänsel, W., Giunta, M., Fischer, M., Lezius, M. & Holzwarth, R. Rapid electro-optic control of the carrier-envelope-offset frequency for ultra-low noise frequency combs. In Proceedings of the Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium 128–129 (IEEE, 2017).

  47. Giunta, M., Hänsel, W., Fischer, M., Lezius, M. & Holzwarth, R. Sub-mHz spectral purity transfer for next generation strontium optical atomic clocks. In Proceedings of the Conference on Lasers and Electro-Optics SM1L.5 (OSA, 2018).

  48. Ma, L. S., 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).

    Article  ADS  Google Scholar 

  49. 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).

    Article  ADS  Google Scholar 

  50. Howe, D. The total deviation approach to long-term characterization of frequency stability. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1102–1110 (2000).

    Article  Google Scholar 

Download references


This work is supported by the National Institute of Standards and Technology (NIST), the Defense Advanced Research Projects Agency (DARPA), the Air Force Office of Scientific Research Multidisciplinary University Research Initiative, the National Science Foundation (NSF) JILA Physics Frontier Center (NSF PHY-1734006), the Cluster of Excellence (EXC 2132 Quantum Frontiers) and Physikalisch-Technische Bundesanstalt (PTB). E.O. and C.J.K. are supported by a postdoctoral fellowship from the National Research Council, L.S. is supported by a National Defense Science and Engineering Graduate Fellowship, A.G. is supported by a fellowship from the Japan Society for the Promotion of Science and C.S. is supported by a fellowship from the Humboldt Foundation. T.L., D.G.M. and U.S. acknowledge support from the Quantum sensors (Q-SENSE) project, supported by the European Commission’s H2020 Marie Skodowska-Curie Actions Research and Innovation Staff Exchange (MSCA RISE) under grant agreement no. 69115. M.G. and R.H. acknowledge support from the EU FP7 initial training network FACT (Future Atomic Clock Technology) and the DARPA Program in Ultrafast Laser Science and Engineering (PμreComb project) under contract no. W31P4Q-14-C-0050. The authors thank J. Munez and J. Sherman for careful reading of this manuscript.

Author information

Authors and Affiliations



E.O., R.B.H., C.J.K., T.B., L.S., C.S., D.K., A.G., J.M.R., G.E.M. and J.Y. contributed to the clock instability measurements. E.O., J.M.R., L.S., C.J.K., T.B., D.K., D.G.M., T.L., F.R., U.S. and J.Y. worked on the Si cavity. L.S. and E.O. commissioned the laser stability transfer set-up based on the Er frequency comb developed by M.G. and R.H. All authors contributed to scientific discussions and the writing of this manuscript.

Corresponding authors

Correspondence to E. Oelker or J. Ye.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary notes and figures.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Oelker, E., Hutson, R.B., Kennedy, C.J. et al. Demonstration of 4.8 × 10−17 stability at 1 s for two independent optical clocks. Nat. Photonics 13, 714–719 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing