# Entanglement on an optical atomic-clock transition

## Abstract

State-of-the-art atomic clocks are based on the precise detection of the energy difference between two atomic levels, which is measured in terms of the quantum phase accumulated over a given time interval1,2,3,4. The stability of optical-lattice clocks (OLCs) is limited both by the interrupted interrogation of the atomic system by the local-oscillator laser (Dick noise5) and by the standard quantum limit (SQL) that arises from the quantum noise associated with discrete measurement outcomes. Although schemes for removing the Dick noise have been recently proposed and implemented4,6,7,8, performance beyond the SQL by engineering quantum correlations (entanglement) between atoms9,10,11,12,13,14,15,16,17,18,19,20 has been demonstrated only in proof-of-principle experiments with microwave clocks of limited stability. The generation of entanglement on an optical-clock transition and operation of an OLC beyond the SQL represent important goals in quantum metrology, but have not yet been demonstrated experimentally16. Here we report the creation of a many-atom entangled state on an OLC transition, and use it to demonstrate a Ramsey sequence with an Allan deviation below the SQL after subtraction of the local-oscillator noise. We achieve a metrological gain of $$4.{4}_{-0.4}^{+0.6}$$ decibels over the SQL by using an ensemble consisting of a few hundred ytterbium-171 atoms, corresponding to a reduction of the averaging time by a factor of 2.8 ± 0.3. Our results are currently limited by the phase noise of the local oscillator and Dick noise, but demonstrate the possible performance improvement in state-of-the-art OLCs1,2,3,4 through the use of entanglement. This will enable further advances in timekeeping precision and accuracy, with many scientific and technological applications, including precision tests of the fundamental laws of physics21,22,23, geodesy24,25,26 and gravitational-wave detection27.

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## Data availability

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

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## Acknowledgements

We thank H. Katori, W. Ketterle, A. Ludlow, M. Lukin, J. Ramette, G. Roati, A. Urvoy, Z. Vendeiro and J. Ye for discussions. This work was supported by NSF, DARPA, ONR and the NSF Center for Ultracold Atoms (CUA). S.C. and A.F.A. acknowledge support from the Swiss National Science Foundation (SNSF). B.B. acknowledges support from the National Science and Engineering Research Council of Canada.

## Author information

Authors

### Contributions

A.K., B.B., C.S., E.P.-P., S.C., A.F.A., Z.L., E.M. and V.V. contributed to the building of the experiment. E.P.-P., S.C. and C.S. led the experimental efforts and simulations. S.C., A.F.A., C.S. and E.P.-P. contributed to the data analysis. V.V. conceived and supervised the experiment. S.C. and V.V. wrote the manuscript. All authors discussed the experiment implementation and results and contributed to the manuscript.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Pedrozo-Peñafiel, E., Colombo, S., Shu, C. et al. Entanglement on an optical atomic-clock transition. Nature 588, 414–418 (2020). https://doi.org/10.1038/s41586-020-3006-1

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