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# An elementary quantum network of entangled optical atomic clocks

## Abstract

Optical atomic clocks are our most precise tools to measure time and frequency1,2,3. Precision frequency comparisons between clocks in separate locations enable one to probe the space–time variation of fundamental constants4,5 and the properties of dark matter6,7, to perform geodesy8,9,10 and to evaluate systematic clock shifts. Measurements on independent systems are limited by the standard quantum limit; measurements on entangled systems can surpass the standard quantum limit to reach the ultimate precision allowed by quantum theory—the Heisenberg limit. Although local entangling operations have demonstrated this enhancement at microscopic distances11,12,13,14,15,16, comparisons between remote atomic clocks require the rapid generation of high-fidelity entanglement between systems that have no intrinsic interactions. Here we report the use of a photonic link17,18 to entangle two 88Sr+ ions separated by a macroscopic distance19 (approximately 2 m) to demonstrate an elementary quantum network of entangled optical clocks. For frequency comparisons between the ions, we find that entanglement reduces the measurement uncertainty by nearly $$\sqrt{2}$$, the value predicted for the Heisenberg limit. Today’s optical clocks are typically limited by dephasing of the probe laser20; in this regime, we find that entanglement yields a factor of 2 reduction in the measurement uncertainty compared with conventional correlation spectroscopy techniques20,21,22. We demonstrate this enhancement for the measurement of a frequency shift applied to one of the clocks. This two-node network could be extended to additional nodes23, to other species of trapped particles or—through local operations—to larger entangled systems.

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## Data availability

Source data for all plots are available. All other data or analysis code that support the plots are available from the corresponding authors upon reasonable request.

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## Acknowledgements

We thank E. R. Clements, R. M. Godun, D. B. Hume and A. M. Steane for helpful discussions and insightful comments on the manuscript. We thank Sandia National Laboratories for supplying the HOA2 ion traps used in these experiments. This work was supported by the UK EPSRC Hub in Quantum Computing and Simulation (EP/T001062/1), the EU Quantum Technology Flagship Project AQTION (No. 820495) and C.J.B.’s UKRI Fellowship (MR/S03238X/1). B.C.N. acknowledges funding from the UK National Physical Laboratory.

## Author information

Authors

### Contributions

D.P.N., B.C.N., P.D., D.M., G.A., R.S. and C.J.B. built and maintained the experimental apparatus. R.S. conceived the experiments. B.C.N. and R.S. carried out the experiments, assisted by D.P.N., P.D., D.M. and G.A. B.C.N., R.S. and D.M.L. analysed the data. B.C.N. and R.S. wrote the manuscript with input from all authors. C.J.B. and D.M.L. secured funding and supervised the work.

### Corresponding authors

Correspondence to B. C. Nichol or R. Srinivas.

## Ethics declarations

### Competing interests

C.J.B. is a director of Oxford Ionics. The remaining authors declare no competing interests.

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Nature thanks David Leibrandt and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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## Supplementary information

### Supplementary Information

Supplementary Sections A–J, including Figs. S1–9.

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Nichol, B.C., Srinivas, R., Nadlinger, D.P. et al. An elementary quantum network of entangled optical atomic clocks. Nature 609, 689–694 (2022). https://doi.org/10.1038/s41586-022-05088-z

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• DOI: https://doi.org/10.1038/s41586-022-05088-z