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.
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All data obtained in the study are available from the corresponding author upon reasonable request.
Nicholson, T. L. et al. Systematic evaluation of an atomic clock at 2 × 10−18 total uncertainty. Nat. Commun. 6, 6896 (2015).
Ushijima, I., Takamoto, M., Das, M., Ohkubo, T. & Katori, H. Cryogenic optical lattice clocks. Nat. Photon. 9, 185–189 (2015).
McGrew, W. F. et al. Atomic clock performance enabling geodesy below the centimetre level. Nature 564, 87–90 (2018).
Brewer, S. M. et al. 27Al+ quantum-logic clock with a systematic uncertainty below 10−18. Phys. Rev. Lett. 123, 033201 (2019).
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).
Vermeer, M. Chronometric levelling. Rep. Finnish Geodetic Inst. 83, 2 (1983).
Pound, R. V. & Snider, J. L. Effect of gravity on gamma radiation. Phys. Rev. 140, B788–B803 (1965).
Takano, T. et al. Geopotential measurements with synchronously linked optical lattice clocks. Nat. Photon. 10, 662–666 (2016).
Grotti, J. et al. Geodesy and metrology with a transportable optical clock. Nat. Phys. 14, 437–441 (2018).
Delva, P. et al. Gravitational redshift test using eccentric Galileo satellites. Phys. Rev. Lett. 121, 231101 (2018).
Herrmann, S. et al. Test of the gravitational redshift with Galileo satellites in an eccentric orbit. Phys. Rev. Lett. 121, 231102 (2018).
Bondarescu, R. et al. Ground-based optical atomic clocks as a tool to monitor vertical surface motion. Geophys. J. Int. 202, 1770–1774 (2015).
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).
Lion, G. et al. Determination of a high spatial resolution geopotential model using atomic clock comparisons. J. Geodesy 91, 597–611 (2017).
Will, C. M. The confrontation between general relativity and experiment. Living Rev. Relativ. 17, 4 (2014).
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).
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).
Koller, S. B. et al. Transportable optical lattice clock with 7 × 10−17 uncertainty. Phys. Rev. Lett. 118, 073601 (2017).
Cao, J. et al. A compact, transportable single-ion optical clock with 7.8 × 10−17 systematic uncertainty. Appl. Phys. B 123, 112 (2017).
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).
Sanner, C. et al. Optical clock comparison for Lorentz symmetry testing. Nature 567, 204–208 (2019).
Derevianko, A. & Pospelov, M. Hunting for topological dark matter with atomic clocks. Nat. Phys. 10, 933–936 (2014).
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).
Arvanitaki, A., Huang, J. & Van Tilburg, K. Searching for dilaton dark matter with atomic clocks. Phys. Rev. D 91, 015015 (2015).
Van Tilburg, K., Leefer, N., Bougas, L. & Budker, D. Search for ultralight scalar dark matter with atomic spectroscopy. Phys. Rev. Lett. 115, 011802 (2015).
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).
Wcisło, P. et al. New bounds on dark matter coupling from a global network of optical atomic clocks. Sci. Adv. 4, eaau4869 (2018).
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).
Ushijima, I., Takamoto, M. & Katori, H. Operational magic intensity for Sr optical lattice clocks. Phys. Rev. Lett. 121, 263202 (2018).
Takamoto, M., Takano, T. & Katori, H. Frequency comparison of optical lattice clocks beyond the Dick limit. Nat. Photon. 5, 288–292 (2011).
Matei, D. G. et al. 1.5 μm lasers with sub-10 mHz linewidth. Phys. Rev. Lett. 118, 263202 (2017).
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).
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).
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).
Takasu, T. RTKLIB: An Open Source Program Package for GNSS Positioning (RTKLIB, accessed 8 July 2019); http://www.rtklib.com/rtklib.htm
King, R. W. & Bock, Y. Documentation for the GAMIT GPS Analysis Software (MIT, 2004).
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).
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.
The authors declare no competing interests.
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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