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Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity


Gyroscopes are essential to many diverse applications associated with navigation, positioning and inertial sensing1. In general, most optical gyroscopes rely on the Sagnac effect—a relativistically induced phase shift that scales linearly with the rotational velocity2,3. In ring laser gyroscopes (RLGs), this shift manifests as a resonance splitting in the emission spectrum, which can be detected as a beat frequency4. The need for ever more precise RLGs has fuelled research activities aimed at boosting the sensitivity of RLGs beyond the limits dictated by geometrical constraints, including attempts to use either dispersive or nonlinear effects5,6,7,8. Here we establish and experimentally demonstrate a method using non-Hermitian singularities, or exceptional points, to enhance the Sagnac scale factor9,10,11,12,13. By exploiting the increased rotational sensitivity of RLGs in the vicinity of an exceptional point, we enhance the resonance splitting by up to a factor of 20. Our results pave the way towards the next generation of ultrasensitive and compact RLGs and provide a practical approach for the development of other classes of integrated sensor.

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Fig. 1: Conceptual illustrations comparing the eigenvalue surfaces associated with Hermitian and non-Hermitian two-level systems.
Fig. 2: Principle of operation of an EP-based He–Ne RLG.
Fig. 3: Bifurcations of complex eigenfrequencies and sensitivity enhancement of EP-based RLG around an EP.
Fig. 4: Measured beat frequency and sensitivity enhancement factor versus rotation rate.
Fig. 5: Transfer functions and estimated rotation rates.

Data availability

All data that support the findings of this study are available within the paper and the Supplementary Information and are available from the corresponding author upon reasonable request.


  1. 1.

    Armenise, M. N., Ciminelli, C., Dell’Olio, F. & Passaro, V. M. Advances in Gyroscope Technologies (Springer, 2010).

  2. 2.

    Post, E. J. Sagnac effect. Rev. Mod. Phys. 39, 475–493 (1967).

    ADS  CAS  Article  Google Scholar 

  3. 3.

    Chow, W. W. et al. The ring laser gyro. Rev. Mod. Phys. 57, 61–104 (1985).

    ADS  Article  Google Scholar 

  4. 4.

    Macek, W. M. & Davis, D. T. M. Jr Rotation rate sensing with traveling-wave ring lasers. Appl. Phys. Lett. 2, 67–68 (1963).

    ADS  Article  Google Scholar 

  5. 5.

    Boyd, R. W. Slow and fast light: fundamentals and applications. J. Mod. Opt. 56, 1908–1915 (2009).

    ADS  Article  Google Scholar 

  6. 6.

    Shahriar, M. S. et al. Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light. Phys. Rev. A 75, 053807 (2007).

    ADS  Article  Google Scholar 

  7. 7.

    Smith, D. D., Chang, H., Arissian, L. & Diels, J. C. Dispersion-enhanced laser gyroscope. Phys. Rev. A 78, 053824 (2008).

    ADS  Article  Google Scholar 

  8. 8.

    Kaplan, A. E. & Meystre, P. Enhancement of the Sagnac effect due to nonlinearly induced nonreciprocity. Opt. Lett. 6, 590–592 (1981).

    ADS  CAS  Article  Google Scholar 

  9. 9.

    Hodaei, H. et al. Enhanced sensitivity at higher-order exceptional points. Nature 548, 187–191 (2017); erratum 551, 658–191 (2017).

    ADS  CAS  Article  Google Scholar 

  10. 10.

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

    ADS  CAS  Article  Google Scholar 

  11. 11.

    Ren, J. et al. Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope. Opt. Lett. 42, 1556–1559 (2017).

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Sunada, S. Large Sagnac frequency splitting in a ring resonator operating at an exceptional point. Phys. Rev. A 96, 033842 (2017).

    ADS  Article  Google Scholar 

  13. 13.

    Grant, M. J. & Digonnet, M. J. F. Loss-gain coupled ring resonator gyroscope. In Proc. SPIE Optical, Opto-Atomic, and Entanglement-Enhanced Precision Metrology Vol. 10934 (SPIE, 2019).

  14. 14.

    Vahala, K. J. Optical microcavities. Nature 424, 839–846 (2003).

    ADS  CAS  Article  Google Scholar 

  15. 15.

    Vollmer, F. & Arnold, S. Whispering-gallery-mode biosensing: label-free detection down to single molecules. Nat. Methods 5, 591–596 (2008).

    CAS  Article  Google Scholar 

  16. 16.

    Lu, T. et al. High sensitivity nanoparticle detection using optical microcavities. Proc. Natl Acad. Sci. USA 108, 5976–5979 (2011).

    ADS  CAS  Article  Google Scholar 

  17. 17.

    Liang, W. et al. Resonant microphotonic gyroscope. Optica 4, 114–117 (2017).

    ADS  Article  Google Scholar 

  18. 18.

    Makris, K. G., El-Ganainy, R., Christodoulides, D. N. & Musslimani, Z. H. Beam dynamics in PT symmetric optical lattices. Phys. Rev. Lett, 100, 103904 (2008).

    ADS  CAS  Article  Google Scholar 

  19. 19.

    Klaiman, S., Gunther, U. & Moiseyev, N. Visualization of branch points in PT-symmetric waveguides. Phys. Rev. Lett, 101, 080402 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  20. 20.

    Moiseyev, N. Non-Hermitian Quantum Mechanics (Cambridge Univ. Press, 2011).

  21. 21.

    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).

    ADS  Article  Google Scholar 

  22. 22.

    El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).

    CAS  Article  Google Scholar 

  23. 23.

    Yariv, A. & Yeh, P. Photonics: Optical Electronics in Modern Communications (Oxford Univ. Press, 2006).

  24. 24.

    Khajavikhan, M., John, K. & Leger, J. R. Experimental measurements of supermodes in superposition architectures for coherent laser beam combining. IEEE J. Quantum Electron. 46, 1221–1231 (2010).

    ADS  CAS  Article  Google Scholar 

  25. 25.

    Hu, J., Sun, X., Agarwal, A. & Kimerling, L. C. Design guidelines for optical resonator biochemical sensors. J. Opt. Soc. Am. B 26, 1032–1041 (2009).

    ADS  CAS  Article  Google Scholar 

  26. 26.

    LIGO Scientific and Virgo Collaboration. GW170104: observation of a 50-solar-mass binary black hole coalescence at redshift 0.2. Phys. Rev. Lett. 118, 221101 (2017).

    ADS  Article  Google Scholar 

  27. 27.

    Collett, M. J., Loudon, R. & Gardiner, C. W. Quantum theory of optical homodyne and heterodyne detection. J. Mod. Opt. 34, 881–902 (1987).

    ADS  CAS  Article  Google Scholar 

  28. 28.

    Mortensen, N. A. et al. Fluctuations and noise-limited sensing near the exceptional point of parity-time-symmetric resonator systems. Optica 5, 1342–1346 (2018).

    ADS  CAS  Article  Google Scholar 

  29. 29.

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

    ADS  CAS  Article  Google Scholar 

  30. 30.

    De Carlo, M., De Leonardis, F. & Passaro, V. M. Design rules of a microscale PT-symmetric optical gyroscope using group IV platform. J. Light. Technol. 36, 3261–3268 (2018).

    Article  Google Scholar 

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We acknowledge support from the US Air Force Office of Scientific Research (FA9550-14-1-0037), Office of Naval Research (N00014-16-1-2640, N00014-18-1-2347, N00014-19-1-2052), National Science Foundation (ECCS1454531, DMR-1420620, ECCS1757025), Army Research Office (W911NF-16-1-0013, W911NF-17-1-0481), US–Israel Binational Science Foundation (BSF) (2016381), DARPA (D18AP00058, HR00111820042, HR00111820038) and the European Commission Project ‘Non-Hermitian Quantum Wave Engineering’ (NHQWAVE, MSCA-RISE 691209). We thank W. Luhs for help in setting up the gyroscope and for performing some of the initial measurements, S. Milady, S. Rotter and K. Vahala for technical discussions, and S. Rotter for supporting this project through funding for A.S.

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All authors contributed equally to this work.

Corresponding author

Correspondence to Mercedeh Khajavikhan.

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The authors declare no competing interests.

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Peer review information Nature thanks Chia Wei Hsu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Supplementary information

Supplementary Information

This file contains information on analytical calculations of the beat frequency for Hermitian and non-Hermitian ring laser gyroscopes using linear and nonlinear coupled mode theory and Jones calculus

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

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