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A nonlinear parity–time-symmetric system for robust phase sensing

Nature Electronics (2026)Cite this article

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Abstract

Parity–time-symmetric systems with loss and gain can be described by non-Hermitian Hamiltonians. In such systems, the inclusion of a nonlinear saturable gain can eliminate the imaginary part of frequency eigenvalues and suppress noise. Consequently, a system biased at an exceptional point can be used to create enhanced sensors. However, exceptional-point frequency sensing typically has a relatively small scaling factor and a limited dynamic range. Here we report a nonlinear parity–time-symmetric system that detects the phase difference between the loss and gain resonators. We show both theoretically and experimentally that the phase difference has a cube-root singularity with a large scaling factor over a wide dynamic range. We create a wearable capacitive temperature sensor based on exceptional-point phase sensing and show that it can measure temperatures from 36 °C to 55.5 °C, which corresponds to a perturbation from 0% to 3.95%, with a maximum normalized sensitivity of 400, an estimated dynamic range of 53.52 dB and an estimated signal-to-noise ratio of 63.8 dB. Compared with an exceptional-point frequency sensing sensor, the sensitivity of our sensor is enhanced by an order of magnitude.

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Fig. 1: PT-symmetric LC systems based on phase sensing.
Fig. 2: Experimental setup and results.
Fig. 3: Measured phase noise spectrum of ~0–2-kHz frequency offset under different perturbations.

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Data availability

The data that support the findings of this study are available via figshare at https://doi.org/10.6084/m9.figshare.29411042 (ref. 45). Source data are provided with this paper.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under grant number 62274030 (L.D.) and the National Natural Science Foundation of China under grant number 61727812 (Q.-A.H.).

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Authors and Affiliations

  1. Key Laboratory of MEMS of the Ministry of Education, Southeast University, Nanjing, China

    Dong-Yan Chen, Lei Dong & Qing-An Huang

Authors
  1. Dong-Yan Chen
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  2. Lei Dong
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  3. Qing-An Huang
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Contributions

Q.-A.H. and L.D. conceived and planned the research. D.-Y.C. and L.D. performed the simulations and experiments. D.-Y.C. and L.D. wrote the paper. Q.-A.H. revised the paper.

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Correspondence to Lei Dong or Qing-An Huang.

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Nature Electronics thanks Martino de Carlo and Jan Wiersig for their contribution to the peer review of this work.

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Supplementary Sections 1–5, Figs. 1–20 and equations (1)–(61).

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Chen, DY., Dong, L. & Huang, QA. A nonlinear parity–time-symmetric system for robust phase sensing. Nat Electron (2026). https://doi.org/10.1038/s41928-025-01542-8

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