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Quantum-enhanced sensing by echoing spin-nematic squeezing in atomic Bose–Einstein condensate

Nature Physics volume 19, pages 1585–1590 (2023)Cite this article

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A Publisher Correction to this article was published on 14 August 2023

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Abstract

Quantum entanglement can provide enhanced measurement precision beyond the standard quantum limit, the highest precision achievable with classical means. However, observations with a large enhancement remain challenging due to experimental limitations in the preparation, control and detection of entanglement. Here we report a nonlinear interferometry protocol with echoed spin-nematic squeezing in a spinor atomic Bose–Einstein condensate. We generate spin-nematic squeezed states through spin-mixing dynamics, an atomic analogue of optical four-wave mixing. The squeezed states are refocused back to the vicinity of the classical initial state by a state-flip operation that resembles spin-echo techniques, which leads to encoded phases preferentially amplified over noise. Using a large ensemble of 26,400 atoms, we observe a sensitivity of 15.6 ± 0.5 dB beyond the standard quantum limit for detecting small-angle Rabi rotation, as well as 16.6 ± 1.1 dB for phase sensing in a Ramsey-like interferometry application. Our results highlight the many-body coherence of spin-nematic squeezed states and point to their possible quantum metrological application in atomic magnetometers, atomic clocks and fundamental tests of Lorentz symmetry violations.

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Fig. 1: Spin-nematic squeezing and its echoed dynamics.
Fig. 2: ESNI for sensing a small-angle Rabi rotation.
Fig. 3: Nonlinear Ramsey-like interferometry for quadrature phase sensing.

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Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

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The codes are available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank L. N. Wu, Y. Q. Zou, X. Y. Luo, J. L. Yu, M. Xue and S. F. Guo for helpful discussions. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11654001, U1930201 and 92265205), the Natural Science Foundation of Zhejiang Province (Grant No. LY22A050002), the Key Area Research and Development Program of GuangDong Province (Grant No. 2019B030330001), the National Key R&D Program of China (Grant Nos. 2018YFA0306504 and 2018YFA0306503) and the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302100).

Author information

Author notes

  1. These authors contributed equally: Tian-Wei Mao, Qi Liu.

Authors and Affiliations

  1. State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, China

    Tian-Wei Mao, Jia-Hao Cao, Feng Chen, Wen-Xin Xu, Meng Khoon Tey & Li You

  2. Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, Paris, France

    Qi Liu

  3. Graduate School of China Academy of Engineering Physics, Beijing, China

    Xin-Wei Li

  4. Frontier Science Center for Quantum Information, Beijing, China

    Meng Khoon Tey & Li You

  5. Collaborative Innovation Center of Quantum Matter, Beijing, China

    Meng Khoon Tey & Li You

  6. Hefei National Laboratory, Hefei, China

    Meng Khoon Tey & Li You

  7. School of Science, Zhejiang University of Science and Technology, Hangzhou, China

    Yi-Xiao Huang

  8. Beijing Academy of Quantum Information Sciences, Beijing, China

    Li You

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Contributions

Y.-X.H., Q.L. and L.Y. conceived this study. T.-W.M., Q.L., J.-H.C. and W.-X.X. performed the experiments and analysed the data. T.-W.M., Q.L., X.-W.L. and F.C. conducted the numerical simulations. T.-W.M., Q.L., Y.-X.H., M.-K.T. and L.Y. wrote the paper.

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Correspondence to Qi Liu, Yi-Xiao Huang or Li You.

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Extended data

Extended Data Fig. 1 Calibration of spin rotation around the \({\hat{Q}}_{0}\) axis.

Spin rotations are realized by adjusting the relative phase between two consecutive MW π pulses, which are resonantly coupled to the clock transition between \(\left\vert 1,0\right\rangle\) and \(\left\vert 2,0\right\rangle\) hyperfine states. The blue dots are experimental results averaged over 10 repetitions and the uncertainty of one standard deviation is smaller than the dot size. The solid line is a fit using trigonometry function which helps to infer the actually accumulated geometric phase from the MW pulses.

Source data

Extended Data Fig. 2 Calibration of small-angle Rabi rotation around \({\hat{L}}_{x}\) axis.

In the experiment, we fix the RF amplitude (A0) of the first one in the composite pulse, while the amplitude (A) of the second one is changed to tune the net rotation angle. This figure shows the dependence of the accumulated phase angle on the amplitude ratio of A/A0.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–9 and Discussion.

Supplementary Data

Experimental data in Supplementary Fig. 8.

Source data

Source Data Fig. 1

Statistical source data.

Source Data Fig. 2

Statistical source data.

Source Data Fig. 3

Statistical source data.

Source Data Extended Data Fig. 1

Statistical source data.

Source Data Extended Data Fig. 2

Statistical source data.

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Mao, TW., Liu, Q., Li, XW. et al. Quantum-enhanced sensing by echoing spin-nematic squeezing in atomic Bose–Einstein condensate. Nat. Phys. 19, 1585–1590 (2023). https://doi.org/10.1038/s41567-023-02168-3

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