# Optical clock comparison for Lorentz symmetry testing

## Abstract

Questioning basic assumptions about the structure of space and time has greatly enhanced our understanding of nature. State-of-the-art atomic clocks1,2,3 make it possible to precisely test fundamental symmetry properties of spacetime and search for physics beyond the standard model at low energies of just a few electronvolts4. Modern tests of Einstein’s theory of relativity try to measure so-far-undetected violations of Lorentz symmetry5; accurately comparing the frequencies of optical clocks is a promising route to further improving such tests6. Here we experimentally demonstrate agreement between two single-ion optical clocks at the 10−18 level, directly validating their uncertainty budgets, over a six-month comparison period. The ytterbium ions of the two clocks are confined in separate ion traps with quantization axes aligned along non-parallel directions. Hypothetical Lorentz symmetry violations5,6,7 would lead to periodic modulations of the frequency offset as the Earth rotates and orbits the Sun. From the absence of such modulations at the 10−19 level we deduce stringent limits of the order of 10−21 on Lorentz symmetry violation parameters for electrons, improving previous limits8,9,10 by two orders of magnitude. Such levels of precision will be essential for low-energy tests of future quantum gravity theories describing dynamics at the Planck scale4, which are expected to predict the magnitude of residual symmetry violations.

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## Data availability

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

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## Acknowledgements

We thank B. Altschul, A. Goban, R. Hutson, A. Kostelecký, T. Mehlstäubler, M. Mewes, A. Vargas-Silva and J. Zhang for discussions and B. Lipphardt for experimental assistance. This research received funding from the European Metrology Programme for Innovation and Research (EMPIR project OC18), co-financed by the Participating States and the European Union’s Horizon 2020 research and innovation programme, and from DFG through CRC 1227 (DQ-mat). This work was also supported in part by the Office of Naval Research, USA, under award number N00014-17-1-2252, by NSF through grant PHY-1620687 (USA) and by the Russian Foundation for Basic Research under grant number 17-02-00216. C.S. thanks the Humboldt Foundation for support.

## Author information

Authors

### Contributions

C.S., N.H. and E.P. conceived the experiment and developed the methods. C.S., N.H., R.L. and C.T. designed and constructed the experimental apparatus. C.S., N.H., R.L., M.S.S. and S.G.P. acquired and analysed the data. All authors were involved in the preparation and discussion of the manuscript.

### Corresponding author

Correspondence to Christian Sanner.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

This file contains details about the transformation between lab frame and celestial frame and derives explicit formulas for the matrix elements of the T0(2) operator.

## Rights and permissions

Reprints and Permissions

Sanner, C., Huntemann, N., Lange, R. et al. Optical clock comparison for Lorentz symmetry testing. Nature 567, 204–208 (2019). https://doi.org/10.1038/s41586-019-0972-2

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