Skip to main content

Thank you for visiting nature.com. 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.

Test of general relativity by a pair of transportable optical lattice clocks

Nature Photonics volume 14, pages 411–415 (2020)Cite this article

Subjects

Abstract

A clock at a higher altitude ticks faster than one at a lower altitude, in accordance with Einstein’s theory of general relativity. The outstanding stability and accuracy of optical clocks, at 10−18 levels1,2,3,4,5, allows height differences6 of a centimetre to be measured. However, such state-of-the-art clocks have been demonstrated only in well-conditioned laboratories. Here, we demonstrate an 18-digit-precision frequency comparison in a broadcasting tower, Tokyo Skytree, by developing transportable optical lattice clocks. The tower provides the clocks with adverse conditions to test the robustness and a 450 m height difference to test the gravitational redshift at (1.4 ± 9.1) × 10−5. The result improves ground-based clock comparisons7,8,9 by an order of magnitude and is comparable with space experiments10,11. Our demonstration shows that optical clocks resolving centimetres are technically ready for field applications, such as monitoring spatiotemporal changes of geopotentials caused by active volcanoes or crustal deformation12 and for defining the geoid13,14, which will have an immense impact on future society.

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

Prices vary by article type

from$1.95

to$39.95

Learn more

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

Fig. 1: Transportable optical lattice clocks.
Fig. 2: Gravitational potential differences investigated by three different methods of chronometric levelling, laser ranging and GNSS complemented by spirit levelling and a gravimeter.
Fig. 3: Height and frequency differences between two clocks.

Data availability

All data obtained in the study are available from the corresponding author upon reasonable request.

References

  1. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. 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 

  5. 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 

  6. Vermeer, M. Chronometric levelling. Rep. Finnish Geodetic Inst. 83, 2 (1983).

    Google Scholar 

  7. Pound, R. V. & Snider, J. L. Effect of gravity on gamma radiation. Phys. Rev. 140, B788–B803 (1965).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  10. Delva, P. et al. Gravitational redshift test using eccentric Galileo satellites. Phys. Rev. Lett. 121, 231101 (2018).

    Article  ADS  Google Scholar 

  11. Herrmann, S. et al. Test of the gravitational redshift with Galileo satellites in an eccentric orbit. Phys. Rev. Lett. 121, 231102 (2018).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. 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. Geodesy 92, 487–516 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Will, C. M. The confrontation between general relativity and experiment. Living Rev. Relativ. 17, 4 (2014).

    Article  ADS  Google Scholar 

  16. Brax, P. What makes the universe accelerate? A review on what dark energy could be and how to test it. Rep. Prog. Phys. 81, 016902 (2017).

    Article  MathSciNet  ADS  Google Scholar 

  17. Smarr, L. L., Vessot, R. F. C., Lundquist, C. A., Decher, R. & Piran, T. Gravitational waves and red shifts: a space experiment for testing relativistic gravity using multiple time-correlated radio signals. Gen. Relativ. Gravit. 15, 129–163 (1983).

    Article  ADS  Google Scholar 

  18. Koller, S. B. et al. Transportable optical lattice clock with 7 × 10−17 uncertainty. Phys. Rev. Lett. 118, 073601 (2017).

    Article  ADS  Google Scholar 

  19. Cao, J. et al. A compact, transportable single-ion optical clock with 7.8 × 10−17 systematic uncertainty. Appl. Phys. B 123, 112 (2017).

    Article  ADS  Google Scholar 

  20. Origlia, S. et al. Towards an optical clock for space: compact, high-performance optical lattice clock based on bosonic atoms. Phys. Rev. A 98, 053443 (2018).

    Article  ADS  Google Scholar 

  21. Sanner, C. et al. Optical clock comparison for Lorentz symmetry testing. Nature 567, 204–208 (2019).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  23. Stadnik, Y. V. & Flambaum, V. V. Searching for dark matter and variation of fundamental constants with laser and maser interferometry. Phys. Rev. Lett. 114, 161301 (2015).

    Article  ADS  Google Scholar 

  24. 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 

  25. Van Tilburg, K., Leefer, N., Bougas, L. & Budker, D. Search for ultralight scalar dark matter with atomic spectroscopy. Phys. Rev. Lett. 115, 011802 (2015).

    Article  ADS  Google Scholar 

  26. Hees, A., Guena, 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).

    Article  ADS  Google Scholar 

  27. Wcisło, P. et al. New bounds on dark matter coupling from a global network of optical atomic clocks. Sci. Adv. 4, eaau4869 (2018).

    Article  ADS  Google Scholar 

  28. 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).

    Article  ADS  Google Scholar 

  29. Ushijima, I., Takamoto, M. & Katori, H. Operational magic intensity for Sr optical lattice clocks. Phys. Rev. Lett. 121, 263202 (2018).

    Article  ADS  Google Scholar 

  30. 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 

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

    Article  ADS  Google Scholar 

  32. Mukaiyama, T., Katori, H., Ido, T., Li, Y. & Kuwata-Gonokami, M. Recoil-limited laser cooling of 87Sr atoms near the Fermi temperature. Phys. Rev. Lett. 90, 113002 (2003).

    Article  ADS  Google Scholar 

  33. Takamoto, M. et al. Improved frequency measurement of a one-dimensional optical lattice clock with a spin-polarized fermionic 87Sr isotope. J. Phys. Soc. Jpn 75, 104302 (2006).

    Article  ADS  Google Scholar 

  34. Alves, B. X. R., Foucault, Y., Vallet, G. & Lodewyck, J. Background gas collision frequency shift on lattice-trapped strontium atoms. In 2019 Joint Conference of the IEEE International Frequency Control Symposium and European Frequency and Time Forum (IEEE, 2019).

  35. Takasu, T. RTKLIB: An Open Source Program Package for GNSS Positioning (RTKLIB, accessed 8 July 2019); http://www.rtklib.com/rtklib.htm

  36. King, R. W. & Bock, Y. Documentation for the GAMIT GPS Analysis Software (MIT, 2004).

  37. Yahagi, T., Yoshida, K., Miyazaki, T., Hiraoka, Y. & Miyahara, B. Construction of the Japan Gravity Standardization Net 2016. Bull. Geospatial Information Authority of Japan 66, 49–58 (2018).

    Google Scholar 

Download references

Acknowledgements

This work received support from a Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Specially Promoted Research (grant no. JP16H06284) and Japan Science and Technology Agency (JST)-Mirai Program grant no. JPMJMI18A1. H.S. acknowledges support from JSPS KAKENHI grant no. JP17H06358. We thank Shimadzu Corporation for development of control electronics for the laser system, Geospatial Information Authority of Japan for GNSS, levelling and gravity measurements, Tobu Tower Skytree Co. for support of the experiments, J. Fortágh and L. Sárkány for the loan of wavelength meters, Y. Takahashi from Citizen Watch Co. for development of a laser system, M. Kokubun for support with electronics, K. Araki for designing control electronics, T. Takahashi, H. Ichikawa and A. Gomyo for laser ranging measurements and A. Hinton for reading the manuscript.

Author information

Authors and Affiliations

  1. Quantum Metrology Laboratory, RIKEN, Wako, Saitama, Japan

    Masao Takamoto, Noriaki Ohmae & Hidetoshi Katori

  2. Space-Time Engineering Research Team, RIKEN, Wako, Saitama, Japan

    Masao Takamoto, Noriaki Ohmae & Hidetoshi Katori

  3. Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo, Japan

    Ichiro Ushijima & Hidetoshi Katori

  4. Geospatial Information Authority of Japan, Tsukuba, Ibaraki, Japan

    Toshihiro Yahagi & Kensuke Kokado

  5. Osaka Institute of Technology, Kitayama, Hirakata, Osaka, Japan

    Hisaaki Shinkai

Authors
  1. Masao Takamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ichiro Ushijima
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Noriaki Ohmae
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Toshihiro Yahagi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kensuke Kokado
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hisaaki Shinkai
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Hidetoshi Katori
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

H.K. envisaged and initiated the experiments. H.K., M.T., I.U. and N.O. designed the apparatus and experiments. I.U., M.T. and N.O. carried out experiments and analysed data. T.Y. and K.K. conducted geodetic measurements. All authors discussed the results and contributed to the writing of the draft.

Corresponding author

Correspondence to Hidetoshi Katori.

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 Figs. 1 and 2 and Supplementary Tables 1 and 2.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Takamoto, M., Ushijima, I., Ohmae, N. et al. Test of general relativity by a pair of transportable optical lattice clocks. Nat. Photonics 14, 411–415 (2020). https://doi.org/10.1038/s41566-020-0619-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-020-0619-8

This article is cited by

Search

Advanced search

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