Abstract
Einstein’s theory of general relativity states that clocks at different gravitational potentials tick at different rates relative to lab coordinates—an effect known as the gravitational redshift1. As fundamental probes of space and time, atomic clocks have long served to test this prediction at distance scales from 30 centimetres to thousands of kilometres2,3,4. Ultimately, clocks will enable the study of the union of general relativity and quantum mechanics once they become sensitive to the finite wavefunction of quantum objects oscillating in curved space-time. Towards this regime, we measure a linear frequency gradient consistent with the gravitational redshift within a single millimetre-scale sample of ultracold strontium. Our result is enabled by improving the fractional frequency measurement uncertainty by more than a factor of 10, now reaching 7.6 × 10−21. This heralds a new regime of clock operation necessitating intra-sample corrections for gravitational perturbations.
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Data availability
The experimental data are available from the corresponding authors upon reasonable request.
Code availability
The code used for the analysis is available from the corresponding authors upon reasonable request.
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Acknowledgements
We acknowledge funding support from the Defense Advanced Research Projects Agency, National Science Foundation QLCI OMA-2016244, the DOE Quantum System Accelerator, the National Institute of Standards and Technology, National Science Foundation Phys-1734006 and the Air Force Office for Scientific Research. We are grateful for theory insight from A. Chu, P. He and A. M. Rey. We acknowledge J. Zaris, J. Uhrich, J. Meyer, R. Hutson, C. Sanner, W. Milner, L. Sonderhouse, L. Yan, M. Miklos, Y. M. Tso and S. Kolkowitz for stimulating discussions and technical contributions. We thank J. Thompson, C. Regal, J. Hall and S. Haroche for careful reading of the manuscript.
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Bothwell, T., Kennedy, C.J., Aeppli, A. et al. Resolving the gravitational redshift across a millimetre-scale atomic sample. Nature 602, 420–424 (2022). https://doi.org/10.1038/s41586-021-04349-7
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DOI: https://doi.org/10.1038/s41586-021-04349-7
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