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Minute-scale Schrödinger-cat state of spin-5/2 atoms

Nature Photonics volume 19, pages 89–94 (2025)Cite this article

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Abstract

Quantum metrology with non-classical states offers a promising route to improved precision in physical measurements. The quantum effects of Schrödinger-cat superpositions or entanglements enable measurement uncertainties to reach below the standard quantum limit. However, the challenge of maintaining a long coherence time for such non-classical states often prevents full exploitation of the quantum advantage in metrology. Here we demonstrate a long-lived Schrödinger-cat state of optically trapped 173Yb (I = 5/2) atoms. The cat state, a superposition of two oppositely directed and furthest-apart spin states, is generated by a nonlinear spin rotation. Protected in a decoherence-free subspace against inhomogeneous light shifts of an optical lattice, the cat state persists for a coherence time of 1.4(1) × 103 s. A magnetic field is measured using Ramsey interferometry, demonstrating a scheme of Heisenberg-limited metrology for atomic magnetometry, quantum information processing and searching for new physics beyond the Standard Model.

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Fig. 1: Principle of the method.
Fig. 2: Set-up and spin dynamics.
Fig. 3: Ramsey interference.
Fig. 4: Sensitivity to a magnetic field.
Fig. 5: The reconstructed Wigner function distribution on the sphere divided into 100 regions along the longitudinal and latitudinal directions.

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Data availability

Source data for Figs. 2–4 are available via Figshare at https://doi.org/10.6084/m9.figshare.24151038 (ref. 58).

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Acknowledgements

We thank D. Sheng and M. Krstají for fruitful discussions, M.-D. Li and W.-K. Hu for contribution to the apparatus during the early stages. This work is supported by the National Natural Science Foundation of China (NSFC) through grant no. 12174371 and the Innovation Program for Quantum Science and Technology through grant no. 2021ZD0303100. C.-L.Z. was supported by the NSFC through grant no. 11922411 and by the Innovation Program for Quantum Science and Technology through grant no. 2021ZD0300203.

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  1. Y. A. Yang

    Present address: JILA, National Institute of Standards and Technology and University of Colorado, Department of Physics, University of Colorado, Boulder, CO, USA

Authors and Affiliations

  1. Hefei National Research Center for Physical Sciences at the Microscale, School of Physical Sciences, University of Science and Technology of China, Hefei, China

    Y. A. Yang, W.-T. Luo, J.-L. Zhang, S.-Z. Wang, Chang-Ling Zou, T. Xia & Z.-T. Lu

  2. Hefei National Laboratory, University of Science and Technology of China, Hefei, China

    Chang-Ling Zou, T. Xia & Z.-T. Lu

  3. CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, China

    Chang-Ling Zou

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Contributions

Y.A.Y., W.-T.L. and J.-L.Z. constructed the experimental apparatus and performed the experiments and simulations. C.-L.Z. made contributions to the theory part. Y.A.Y., W.-T.L., J.-L.Z., S.-Z.W., C.-L.Z., T.X. and Z.-T.L. carried out data analysis and wrote the manuscript.

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Extended data

Extended Data Fig. 1 Polarizabilities and effective Rabi frequencies.

a, the dynamical vector and tensor polarizabilities \({\alpha }_{F}^{\{{\rm{V}},{\rm{T}}\}}\) of 1S0 are plotted as a function of the laser frequency, whose value is relative to the \(6{{\rm{s}}{}^{2}}^{1}{{\rm{S}}}_{0}\to 6{\rm{s}}6{{\rm{p}}}^{3}{{\rm{P}}}_{1},F=5/2\to F=3/2\) hyperfine transition. For polarizabilities 1a. u. = 1.648773 × 10−41 C m2 V−1. b, The generalized Rabi frequencies \({\Omega }_{x}^{(1)}\) and \({\Omega }_{x,x}^{(2)}\) are plotted as a function of the laser frequency, where \({\Omega }_{x}^{(1)}=-\frac{{\alpha }_{F}^{V}}{8F}{| {\mathcal{E}}| }^{2}\) and \({\Omega }_{x,x}^{(2)}=\frac{3{\alpha }_{F}^{T}}{8F(2F-1)}{| {\mathcal{E}}| }^{2}\). The Rabi frequencies are normalized assuming a light intensity I of = 1W/cm2, and \({| {\mathcal{E}}| }^{2}=\frac{2I}{{\epsilon }_{0}c}\). The inset shows the frequency ratio \(| {\Omega }_{x}^{(1)}/{\Omega }_{x,x}^{(2)}|\).

Extended Data Fig. 2 Principal of state-selective measurement.

The tensor light shift induced by the trap laser distinctly separates Zeeman sublevels of the upper state 3P1, effectively preventing photon absorption by the \(\left\vert -5/2\right\rangle\) state. Following the measurement of the population of the \(\left\vert +5/2\right\rangle\) state, a π pulse generated by the control laser swaps the populations of the \(\left\vert +5/2\right\rangle\) and \(\left\vert -5/2\right\rangle\) states. Subsequently, the same probe pulse is applied to detect the population of the original \(\left\vert -5/2\right\rangle\) state.

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Yang, Y.A., Luo, WT., Zhang, JL. et al. Minute-scale Schrödinger-cat state of spin-5/2 atoms. Nat. Photon. 19, 89–94 (2025). https://doi.org/10.1038/s41566-024-01555-3

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