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  • Open Access

Observation of a phase shift in nonlinear parity-time symmetric film bulk acoustic resonators

Zhenyu Wei, Jian-Qiu Huang*, Mengting Wang, and Qing-An Huang†

  • *Contact author: hjq@seu.edu.cn
  • †Contact author: hqa@seu.edu.cn
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Phys. Rev. Research 7, 043350 – Published 31 December, 2025

DOI: https://doi.org/10.1103/7vrg-tmys

Abstract

An exceptional point (EP) in PT (parity-time)-symmetric systems featuring loss and nonlinear saturable gain has been recently utilized to enhance sensing, leading to the cube-root singularity in a two-level system. However, a shift in the frequency eigenvalue comes with a relatively small scaling factor, which could potentially reduce the sensitivity augmented by the cube-root singularity, and achieving the cube-root singularity necessitates sacrificing the sensing dynamic range. Instead of detecting frequency eigenvalue, this article explores the phase shift between both resonators in parity-time symmetric film bulk acoustic resonators (FBARs) with a nonlinear saturable gain. When the FBAR is linked to an external (inductor-capacitor loop with a nonlinear negative resistance, it forms PT-symmetric resonators with loss and nonlinear gain. Our findings show that the phase difference between the loss and gain resonators displays both a cube-root dependence on perturbation and an increased scaling factor. Experimental results from our FBAR humidity sensors indicate that the sensitivity of phase shift has increased by several orders of magnitude compared to the conventional frequency shift. These discoveries have potential applications for piezoelectric resonant sensors requiring ultrahigh sensitivity across various fields.

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References (51)

  1. G. Sauerbrey, Verwendung von Schwingquartzen zur Wägung dünner Schichten und zur Mikrowägung, Z. Phys. 155, 206 (1959).
  2. M. D. Ward and D. A. Buttry, In situ interfacial mass detection with piezoelectric transducers, Science 249, 1000 (1990).
  3. K. Bodenhöfer, A. Hierlemann, J. Seemann, G. Gauglitz, B. Koppenhoefer, and W. Göpel, Chiral discrimination using piezoelectric and optical gas sensors, Nature (London) 387, 577 (1997).
  4. C. Steinem and A. Janshoff, Piezoelectric Sensors (Springer, Berlin, 2007).
  5. P. Lieberzeit, Piezoelectric Sensors (Springer, Berlin, 2024).
  6. R. Gabl, E. Green, M. Schreiter, H. D. Feucht, H. Zeininger, R. Primig, D. Pitzer, G. Eckstein, and W. Wersing, Novel integrated FBAR sensors: A universal technology platform for bio- and gas-detection, in Proceedings of the 2nd IEEE Conference on Sensors (IEEE Press, Toronto, 2003), pp. 1184–1188.
  7. W. Pang, H. Y. Zhao, E. S. Kim, H. Zhang, H. Y. Yu, and X. T. Hu, Piezoelectric microelectromechanical resonant sensors for chemical and biological detection, Lab Chip 12, 29 (2012).
  8. Y. Zhang, J. K. Luo, A. J. Flewitt, Z. Q. Cai, and X. B. Zhao, Film bulk acoustic resonators (FBARs) as biosensors: A review, Biosens. Bioelectron. 116, 1 (2018).
  9. A. K.Johar, G. K. Sharma, J. K. Bhatt, A. Kumar, P. Singh, T. Varma, C. Periasamy, A. Agarwal, and D. Boolchandani, VOCs sensors based on bulk acoustic resonators: A comprehensive review, Microsyst. Technol. 30, 821 (2024).
  10. D. Pareek Vinita, S. M. Islam, and J. Singh, Bulk acoustic wave resonators for sensing applications: A review, Sens. Actuators A 378, 115839 (2024).
  11. T. Kato, Perturbation Theory for Linear Operators (Springer, Berlin, 1966).
  12. C. M. Bender, PT Symmetry in Quantum and Classical Physics (World Scientific Publishing, Singapore, 2019).
  13. D. Christodoulides and J. Yang, Parity-Time Symmetry and Its Applications (Springer, Singapore, 2018).
  14. W. D. Heiss, The physics of exceptional points, J. Phys. A: Math. Theor. 45, 444016 (2012).
  15. M.-A. Miri and A. Alù, Exceptional points in optics and photonics, Science 363, eaar7709 (2019).
  16. Ş. K. Özdemir, S. Rotter, F. Nori, and L. Yang, Parity-time symmetry and exceptional points in photonics, Nat. Mater. 18, 783 (2019).
  17. A. Li, H. Wei, M. Cotrufo, W. Chen, S. Mann, X. Ni, B. Xu, J. Chen, J. Wang, S. Fan, C. W. Qiu, A. Alù, and L. Chen, Exceptional points and non-Hermitian photonics at the nanoscale, Nat. Nanotechnol. 18, 706 (2023).
  18. J. Wiersig, 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).
  19. J. Wiersig, Review of exceptional point-based sensors, Photonics Res. 8, 1457 (2020).
  20. H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, Enhanced sensitivity at higher-order exceptional points, Nature (London) 548, 187 (2017).
  21. W. Chen, S. K. Ozdemir, G. Zhao, J. Wiersig, and L. Yang, Exceptional points enhance sensing in an optical microcavity, Nature (London) 548, 192 (2017).
  22. M. P. Hokmabadi, A. Schumer, D. N. Christodoulides, and M. Khajavikhan, Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity, Nature (London) 576, 70 (2019).
  23. Y.-H. Lai, Y.-K. Lu, M.-G. Suh, Z. Yuan, and K. Vahala, Observation of the exceptional-point-enhanced Sagnac effect, Nature (London) 576, 65 (2019).
  24. W. B. Mao, Z. T. Fu, Y. H. Li, F. Li, and L. Yang, Exceptional-point-enhanced phase sensing, Sci. Adv. 10, eadl5037 (2024).
  25. J.-H. Park, A. Ndao, W. Cai, L. Hsu, A. Kodigala, T. Lepetit, Y.-H. Lo, and B. Kanté, Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing, Nat. Phys. 16, 462 (2020).
  26. P. Y. Chen, M. Sakhdari, M. Hajizadegan, Q. Cui, M. M. C. Cheng, R. El-Ganainy, and A. Alù, Generalized parity-time symmetry condition for enhanced sensor telemetry, Nat. Electron. 1, 297 (2018).
  27. Z. Dong, Z. Li, F. Yang, C.-W. Qiu, and J. S. Ho, Sensitive readout of implantable microsensors using a wireless system locked to an exceptional point, Nat. Electron. 2, 335 (2019).
  28. B. B. Zhou, L. F. Wang, L. Dong, and Q. A. Huang, Observation of the perturbed eigenvalues of PT-symmetric LC resonator systems, J. Phys. Commun. 5, 045010 (2021).
  29. R. Kononchuk, J. Cai, F. Ellis, R. Thevamaran, and T. Kottos, Exceptional-point-based accelerometers with enhanced signal-to-noise ratio, Nature (London) 607, 697 (2022).
  30. M. N. Zhang, L. Dong, L. F. Wang, and Q. A. Huang, Exceptional points enhance sensing in silicon micromechanical resonators, Microsyst. Nanoeng. 10, 12 (2024).
  31. L. F. Wang, S. Y. Zhang, and Q. Yuan, Strain-induced frequency splitting in PT symmetric coupled silicon resonators, Micromachines 15, 1278 (2024).
  32. W. Langbein, No exceptional precision of exceptional-point sensors, Phys. Rev. A 98, 023805 (2018).
  33. H.-K. Lau and A. A. Clerk, Fundamental limits and non-reciprocal approaches in non-Hermitian quantum sensing, Nat. Commun. 9, 4320 (2018).
  34. J. Wiersig, Prospects and fundamental limits in exceptional point-based sensing, Nat. Commun. 11, 2454 (2020).
  35. H. Wang, Y.-H. Lai, Z. Yuan, M.-G. Suh, and K. Vahala, Petermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope, Nat. Commun. 11, 1610 (2020).
  36. R. Duggen, S. Mann, and A. Alú, Limitations of sensing at an exceptional point, ACS Photonics 9, 1554 (2022).
  37. D. Anderson, M. Shah, and L. R. Fan, Clarification of the exceptional-point contribution to photonic sensing, Phys. Rev. Appl. 19, 034059 (2023).
  38. H. Loughlin and V. Sudhir, Exceptional-point sensors offer no fundamental signal-to-noise ratio enhancement, Phys. Rev. Lett. 132, 243601 (2024).
  39. S. Assawaworrarit, X. Yu, and S. Fan, Robust wireless power transfer using a nonlinear parity–time-symmetric circuit, Nature (London) 546, 387 (2017).
  40. A. Nikzamir and F. Capolino, Highly sensitive coupled oscillator based on an exceptional point of degeneracy and nonlinearity, Phys. Rev. Appl. 18, 054059 (2022).
  41. A. Suntharalingam, L. Fernández-Alcázar, R. Kononchuk, and T. Kottos, Noise resilient exceptional-point voltmeters enabled by oscillation quenching phenomena, Nat. Commun. 14, 5515 (2023).
  42. K. Bai, T.-R. Liu, L. Fang, J.-Z. Li, C. Lin, D. Wan, and M. Xiao, Observation of nonlinear exceptional points with a complete basis in dynamics, Phys. Rev. Lett. 132, 073802 (2024).
  43. D. Y. Chen, L. Dong, and Q. A. Huang, Inductor-capacitor passive wireless sensors using nonlinear parity-time symmetric configurations, Nat. Commun. 15, 9312 (2024).
  44. Z. Wei, J. Q. Huang, M. Wang, W. Xu, and Q. A. Huang, Exceptional precision of a piezoelectric resonance sensor at a cube-root singularity, Phys. Rev. Appl. 22, 064082 (2024).
  45. See Supplemental Material at https://link.aps.org/supplemental/10.1103/7vrg-tmys for operations of two coupled LC resonators, ADS simulation, and experiments.
  46. J.-Y. Park and J.-W. Choi, Review: Electronic circuit systems for piezoelectric resonance sensors, J. Electrochem. Soc. 167, 037560 (2020).
  47. J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, PT-symmetric electronics, J. Phys. A: Math. Gen. 45, 444029 (2012).
  48. Z. H. Duan, Y. D. Jiang, and H. L. Tai, Recent advances in humidity sensors for human body related humidity detection, J. Mater. Chem. C 9, 14963 (2021).
  49. D. Kim, J. Lee, M. K. Park, and S. H. Ko, Recent developments in wearable breath sensors for healthcare monitoring, Commun. Mater. 5, 41 (2024).
  50. S. Xu, J. He, Z. Y. Wei, and J. Q. Huang, Microbalance humidity sensors based on electrospun graphene oxide composites, in Proceedings of the 21st IEEE Conference on Sensors (IEEE Press, Dallas, TX, 2022), pp. 1–4.
  51. M. T. Wang, J. Q. Huang, and Q. A. Huang, Putting piezoelectric sensors into Fano resonances, Microsyst. Nanoeng. 10, 202 (2024).

Outline

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Phys. Rev. Research 7, 043350– Published 31 December, 2025
  • Received 22 August 2025
  • Accepted 15 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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