Abstract
Neutral-atom arrays trapped in optical potentials are a powerful platform for studying quantum physics, combining precise single-particle control and detection with a range of tunable entangling interactions1,2,3. For example, these capabilities have been leveraged for state-of-the-art frequency metrology4,5 as well as microscopic studies of entangled many-particle states6,7,8,9,10,11. Here we combine these applications to realize spin squeezing—a widely studied operation for producing metrologically useful entanglement—in an optical atomic clock based on a programmable array of interacting optical qubits. In this demonstration of Rydberg-mediated squeezing with a neutral-atom optical clock, we generate states that have almost four decibels of metrological gain. In addition, we perform a synchronous frequency comparison between independent squeezed states and observe a fractional-frequency stability of 1.087(1) × 10−15 at one-second averaging time, which is 1.94(1) decibels below the standard quantum limit and reaches a fractional precision at the 10−17 level during a half-hour measurement. We further leverage the programmable control afforded by optical tweezer arrays to apply local phase shifts to explore spin squeezing in measurements that operate beyond the relative coherence time with the optical local oscillator. The realization of this spin-squeezing protocol in a programmable atom-array clock will enable a wide range of quantum-information-inspired techniques for optimal phase estimation and Heisenberg-limited optical atomic clocks12,13,14,15,16.
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Data availability
The experimental data presented in this article are available from the corresponding author upon reasonable request. Source data are provided with this paper.
Code availability
The code used for analysis and simulation in this work is available from the corresponding author upon reasonable request.
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Acknowledgements
We acknowledge earlier contributions to the experiment from M. A. Norcia and N. Schine and discussions with S. Geller, R. B. Hutson, W. F. McGrew, S. R. Muleady, A. M. Rey, N. Schine, M. Schleier-Smith, J. K. Thompson, J. T. Young and P. Zoller. We thank S. Geller, S. R. Muleady, J. K. Thompson and P. Zoller for reading the paper and comments; and A. Aeppli, D. Kedar, K. Kim, B. Lewis, M. Miklos, Y. M. Tso, W. Warfield, L. Yan and Z. Yao for discussions and contributions to the clock laser system. This material is based on work supported by the Army Research Office (W911NF-19-1-0149 and W911NF-19-1-0223), Air Force Office for Scientific Research (FA9550-19-1-0275), National Science Foundation QLCI (OMA-2016244), US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, and the National Institute of Standards and Technology. We also acknowledge funding from Lockheed Martin. W.J.E. acknowledges support from the NDSEG Fellowship; N.D.O. acknowledges support from the Alexander von Humboldt Foundation; and A.C. acknowledges support from the NSF Graduate Research Fellowship Program (grant number DGE2040434).
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W.J.E., N.D.O., A.C., A.W.Y. and A.M.K. built and operated the optical lattice and tweezer apparatus. The silicon-crystal stabilized clock laser was operated by W.R.M., J.M.R. and J.Y. All authors contributed to data analysis and development of the paper.
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Eckner, W.J., Darkwah Oppong, N., Cao, A. et al. Realizing spin squeezing with Rydberg interactions in an optical clock. Nature 621, 734–739 (2023). https://doi.org/10.1038/s41586-023-06360-6
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DOI: https://doi.org/10.1038/s41586-023-06360-6
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