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


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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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.


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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.

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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.

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Correspondence to Hidetoshi Katori.

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

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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).

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