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Exceptional-point-based accelerometers with enhanced signal-to-noise ratio

An Author Correction to this article was published on 09 March 2023

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Exceptional points (EP) are non-Hermitian degeneracies where eigenvalues and their corresponding eigenvectors coalesce1,2,3,4. Recently, EPs have attracted attention as a means to enhance the responsivity of sensors, through the abrupt resonant detuning occurring in their proximity5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20. In many cases, however, the EP implementation is accompanied by noise enhancement, leading to the degradation of the sensor’s performance15,16,17,18,19,20. The excess noise can be of fundamental nature (owing to the eigenbasis collapse) or of technical nature associated with the amplification mechanisms utilized for the realization of EPs. Here we show, using an EP-based parity–time symmetric21,22 electromechanical accelerometer, that the enhanced technical noise can be surpassed by the enhanced responsivity to applied accelerations. The noise owing to eigenbasis collapse is mitigated by exploiting the detuning from a transmission peak degeneracy (TPD) — which forms when the sensor is weakly coupled to transmission lines — as a measure of the sensitivity. These TPDs occur at a frequency and control parameters for which the biorthogonal eigenbasis is still complete and are distinct from the EPs of the parity–time symmetric sensor. Our device shows a threefold signal-to-noise-ratio enhancement compared with configurations for which the system operates away from the TPD.

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Fig. 1: \(\boldsymbol{\mathscr{P}}\boldsymbol{\mathscr{T}}\)-symmetric platform for enhanced acceleration sensing.
Fig. 2: Experimentally measured response of the sensor to applied acceleration.
Fig. 3: Measured Allan deviation.

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Data availability

The datasets generated during and/or analysed during the current study are available in the Zenodo repository at

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  1. Kato, T. Perturbation Theory for Linear Operators (Springer, 2013).

  2. Berry, M. V. Physics of nonhermitian degeneracies. Czech. J. Phys. 54, 1039–1047 (2004).

    Article  ADS  CAS  Google Scholar 

  3. Miri, M.-A. & Alu, A. Exceptional points in optics and photonics. Science 363, eaar7709 (2019).

    Article  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  4. Parto, M., Liu, Y. G. N., Bahari, B., Khajavikhan, M. & Christodoulides, D. N. Non-Hermitian and topological photonics: optics at an exceptional point. Nanophotonics 10, 403 (2021).

    Article  Google Scholar 

  5. Wiersig, J. Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection. Phys. Rev. Lett. 112, 203901 (2014).

    Article  ADS  Google Scholar 

  6. Hodaei, H. et al. Enhanced sensitivity at higher-order exceptional points. Nature 548, 187–191 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  7. Chen, W., Ozdemir, S. K., Zhao, G., Wiersig, J. & Yang, L. Exceptional points enhance sensing in an optical microcavity. Nature 548, 192–196 (2017).

    Article  ADS  CAS  PubMed  Google Scholar 

  8. Chen, P.-Y. et al. Generalized parity–time symmetry condition for enhanced sensor telemetry. Nat. Electron. 1, 297–304 (2018).

    Article  Google Scholar 

  9. Dong, Z., Li, Z., Yang, F., Qiu, C.-W. & Ho, J. S. Sensitive readout of implantable microsensors using a wireless system locked to an exceptional point. Nat. Electron. 2, 335–342 (2019).

    Article  Google Scholar 

  10. Hokmabadi, M. P., Schumer, A., Christodoulides, D. N. & Khajavikhan, M. Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity. Nature 576, 70–74 (2019).

    Article  ADS  PubMed  Google Scholar 

  11. Kononchuk, R. & Kottos, T. Orientation-sensed optomechanical acelerometers based on exceptional points. Phys. Rev. Res. 2, 023252 (2020).

    Article  CAS  Google Scholar 

  12. Park, J.-H. et al. Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing. Nat. Phys. 16, 462–468 (2020).

    Article  CAS  Google Scholar 

  13. Xiao, Z., Li, H., Kottos, T. & Alú, A. Enhanced sensing and nondegrated thermal noise performance based on \({\mathscr{P}}{\mathscr{T}}\)-symmetric electronic circuits with a sixth-order exceptional point. Phys. Rev. Lett. 123, 213901 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  14. Zhang, M. et al. Quantum noise theory of exceptional point amplifying sensors. Phys. Rev. Lett. 123, 180501 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  15. Lau, H.-K. & Clerk, A. A. Fundamental limits and non-reciprocal approaches in non-Hermitian quantum sensing. Nat. Commun. 9, 4320 (2018).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  16. Wiersig, J. Prospects and fundamental limits in exceptional point-based sensing. Nat. Commun. 11, 2454 (2020).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  17. Lai, Y.-H., Lu, Y.-K., Suh, M.-G., Yuan, Z. & Vahala, K. Observation of the exceptional-point-enhanced Sagnac effect. Nature 576, 65–69 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  18. Wang, H., Lai, Y.-H., Yuan, Z., Suh, M.-G. & Vahala, K. Petermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope. Nat. Commun. 11, 1610 (2020).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  19. Langbein, W. No exceptional precision of exceptional-point sensors. Phys. Rev. A 98, 023805 (2018).

    Article  ADS  CAS  Google Scholar 

  20. Wiersig, J. Robustness of exceptional point-based sensors against parametric noise: the role of Hamiltonian and Liouvillian degeneracies. Phys. Rev. A 101, 053846 (2020).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  21. Schindler, J. et al. PT-symmetric electronics. J. Phys. A 45, 444029 (2012).

    Article  MATH  Google Scholar 

  22. Bender, C. M. & Böttcher, S. Real spectra in non-Hermitian Hamiltonians having \({\mathscr{P}}{\mathscr{T}}\) symmetry. Phys. Rev. Lett. 80, 5243 (1998).

    Article  ADS  MathSciNet  CAS  MATH  Google Scholar 

  23. Fraden, J. in Handbook of Modern Sensors, Chapter 2 (Springer, 2016).

  24. Xiao, G. & Bock, W. J. Photonic Sensing: Principles and Applications for Safety and Security Monitoring (Wiley Series in Microwave and Optical Engineering, Wiley, 2012).

  25. Bao, M. Micro Mechanical Transducers: Pressure Sensors, Accelerometers and Gyroscopes (Elsevier, 2000).

  26. De Brito Andre, P. S. & Humberto, V. Accelerometers: Principles, Structure and Applications (Nova Science, 2013).

  27. Wen, H. et al. Slow-light fiber-Bragg-grating strain sensor with a 280-femtostrain/\(\sqrt{{\rm{Hz}}}\)} resolution. J. Light. Technol 31, 11 (2013).

    Google Scholar 

  28. Skolianos, G., Aurora, A., Bernier, M. & Digonnet, M. J. Slow light in Bragg gratings and its applications. J. Phys. D 49, 463001 (2016).

    Article  Google Scholar 

  29. Geng, Q. & Zhu, K.-D. Discrepancy between transmission spectrum splitting and eigenvalue splitting: a reexamination on exceptional point-based sensors. Photon. Res. 9, 1645–1649 (2021).

    Article  Google Scholar 

  30. Sweeney, W. R., Hsu, C. W., Rotter, S. & Stone, A. D. Perfectly absorbing exceptional points and chiral absorbers. Phys. Rev. Lett. 122, 093901 (2019).

    Article  ADS  CAS  Google Scholar 

  31. Sweeney, W. R., Hsu, C. W. & Stone, A. D. Theory of reflectionless scattering modes. Phys. Rev. A 102, 063511 (2020).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  32. Yoo, G., Sim, H.-S. & Schomerus, H. Quantum noise and mode nonorthogonality in non-Hermitian \({\mathscr{P}}{\mathscr{T}}\) -symmetric optical resonators. Phys. Rev. A 84, 063833 (2011).

    Article  ADS  Google Scholar 

  33. Krause, A. G., Winger, M. T., Blasius, D., Lin, Q. & Painter, O. A high-resolution microchip optomechanical accelerometer. Nat. Photon. 6, 768–772 (2012).

    Article  ADS  CAS  Google Scholar 

  34. Li, Y. L. & Barker, P. F. Characterization and testing of a micro-g whispering gallery mode optomechanical accelerometer. J. Light. Technol. 36, 3919–3926 (2018).

    Article  ADS  CAS  Google Scholar 

  35. Regal, C. A., Teufel, J. D. & Lehnert, K. W. Measuring nanomechanical motion with a microwave cavity interferometer. Nat. Phys. 4, 555–560 (2008).

    Article  CAS  Google Scholar 

  36. El-Sheimy, N., Hou, H. & Niu, X. Analysis and modeling of inertial sensors using Allan variance. IEEE Trans. Instrum. Meas. 57, 140–149 (2008).

    Article  ADS  Google Scholar 

  37. Quinchia, A. G., Falco, G., Falletti, E., Dovis, F. & Ferrer, C. A comparison between different error modeling of MEMS applied to GPS/INS integrated systems. Sensors 13, 9549–9588 (2013).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  38. Duggen, R., Mann, S. & Alú, A. Limitations of sensing at an exceptional point. ACS Photon. 9, 1554–1566 (2022).

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We acknowledge partial support from NSF-CMMI-1925543, NSF-CMMI-1925530, ONR N00014-19-1-2480 and from a grant from Simons Foundation for Collaboration in MPS number 733698. R.T. and J.C. acknowledge the partial support for this research provided by the University of Wisconsin-Madison, Office of the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation.

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Authors and Affiliations



R.K., J.C., F.E. and R.T. designed the mechanical device. R.K. and F.E. designed and fabricated the electronic circuit. J.C. and R.T. fabricated the mechanical device. R.K. performed the characterization and data processing of the accelerometer and developed the theory with the support of T.K. All authors discussed the results. T.K. conceived the project. R.K. and T.K. wrote the manuscript with input from all authors.

Corresponding author

Correspondence to Tsampikos Kottos.

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Nature thanks Jan Wiersig and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Schematic of the circuit diagram.

The dark grey large boxes indicate the ADA4862- 3 operational amplifiers, while the light grey box indicates the spring mass which provides the acceleration dependent capacitance \({C}_{{cv}}\).

Extended Data Fig. 2 Details of the mechanical sensor elements.

a,b, Drawings of the copper platform. c,d, Drawings of the test mass.

Extended Data Fig. 3 Assembly process of the acceleration capacitive sensor.

a, Deposition of the gold nanofilms on a glass substrate that create conductive electrodes which form the capac- itors plates. Attachment of the glass plates to the stationary platform and test mass. b, Placement of the test mass with glass plate on top of the copper base. c, Assembled capacitive inertial sensor. The inset shows the magnified view of the area between the capacitor plates which is about 20 m.

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Supplementary Information

This file contains Supplementary text, figures, equations and references.

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Kononchuk, R., Cai, J., Ellis, F. et al. Exceptional-point-based accelerometers with enhanced signal-to-noise ratio. Nature 607, 697–702 (2022).

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