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Exceptional sensitivity near the bistable transition point of a hybrid quantum system

Nature Physics (2026)Cite this article

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Abstract

Phase transitions can dramatically alter system dynamics, potentially improving device performance. Exceptional points, in which the eigenvalues and corresponding eigenvectors of a coupled linear system coalesce, are particularly relevant for sensing applications because they can increase sensor response to external perturbations. However, the coalescence of eigenstates at linear exceptional points amplifies noise, negating the signal-to-noise-ratio enhancement. Here we overcame this limitation using nonlinearity that produces an exceptionally high signal-to-noise ratio around a bistable transition point. We coupled a diamond nitrogen-vacancy quantum sensor to a nonlinear van der Pol oscillator, forming a self-oscillating hybrid system that exhibits both single-valued and bistable phases. The boundaries between these phases are marked by both adiabatic and deterministic non-adiabatic transitions that enable chiral state switching and state coalescence at the bistable transition point. Nitrogen-vacancy magnetometry performed near the bistable transition point exhibited a 17-fold enhancement in the signal-to-noise ratio. The demonstrated sensitivity surpassed the limit of an ideal bare electron magnetometer and resolved a long-standing debate regarding exceptional-point-like physics in advanced quantum sensing.

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Fig. 1: NV–vdP hybrid system description.
Fig. 2: NV–vdP spectroscopy.
Fig. 3: Dynamically encircling the BP.
Fig. 4: BP-enhanced magnetometry.

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Data availability

The data that support the findings of this study are available via GitHub at https://github.com/hanfengw/BPNV.git. Source data are provided with this paper.

Code availability

The code supporting the findings of this study is available from the corresponding author upon request.

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Acknowledgements

We thank R. Wilcox and S. Wu for their helpful discussions. H.W. acknowledges support from Bosch Inc. and Honda Research Institute USA, Inc. D.R.E. acknowledges funding from the MITRE Corporation.

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Authors and Affiliations

  1. Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Hanfeng Wang, Yong Hu, Dirk R. Englund & Matthew E. Trusheim

  2. DEVCOM Army Research Laboratory, Adelphi, MD, USA

    Kurt Jacobs, Donald Fahey & Matthew E. Trusheim

  3. Department of Physics, University of Massachusetts Boston, Boston, MA, USA

    Kurt Jacobs

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  1. Hanfeng Wang
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Contributions

H.W. and M.E.T. created the set-up and conducted the experiments. H.W., K.J. and M.E.T. developed the theory. D.F. and M.E.T. conducted the preliminary experiment. H.W. and M.E.T. prepared the paper. Y.H. assisted with the time-domain measurements. All authors discussed the results and revised the paper. M.E.T. and D.R.E. supervised the project.

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Correspondence to Hanfeng Wang or Matthew E. Trusheim.

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Nature Physics thanks Dmitry Budker, Jingyan Xu, Chong Zu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Setup for NV-VdP hybrid system.

a, The experimental setup for the NV-VdP system, we use a microwave cavity and two coupling loops to form a loop oscillator, we use a directional coupler to direct the signal out, this signal is then directed to a heterodyne measurement, where an external signal generator is used to move the microwave signal to an intermediate frequency with a frequency of several MHz. We use a series of amplifiers and attenuators to reach a low microwave input to the system so that the spin is not saturated for the NV-cQED system. b, COMSOL simulation for the dielectric resonator. Our dielectric resonator contains two cylinder with outer diameter: 0.669 inch; inner diameter: 0.236 inch; Thickness: 0.314 inch. c, The cavity measurement with critical coupling.

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Wang, H., Jacobs, K., Fahey, D. et al. Exceptional sensitivity near the bistable transition point of a hybrid quantum system. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03217-3

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