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Observation of the exceptional-point-enhanced Sagnac effect

Abstract

Exceptional points (EPs) are special spectral degeneracies of non-Hermitian Hamiltonians that govern the dynamics of open systems. At an EP, two or more eigenvalues, and the corresponding eigenstates, coalesce1,2,3. Recently, it was predicted that operation of an optical gyroscope near an EP results in improved response to rotations4,5. However, the performance of such a system has not been examined experimentally. Here we introduce a precisely controllable physical system for the study of non-Hermitian physics and nonlinear optics in high-quality-factor microresonators. Because this system dissipatively couples counter-propagating lightwaves within the resonator, it also functions as a sensitive gyroscope for the measurement of rotations. We use our system to investigate the predicted EP-enhanced Sagnac effect4,5 and observe a four-fold increase in the Sagnac scale factor by directly measuring rotations applied to the resonator. The level of enhancement can be controlled by adjusting the system bias relative to the EP, and modelling results confirm the observed enhancement. Moreover, we characterize the sensitivity of the gyroscope near the EP. Besides verifying EP physics, this work is important for the understanding of optical gyroscopes.

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Fig. 1: Brillouin control of state vectors in a non-Hermitian system.
Fig. 2: Measurement of the eigenmode properties.
Fig. 3: Measured Sagnac scale factor Sωp) compared with model results.
Fig. 4: Allan deviation of the gyroscope readout at various bias points.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. 1.

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

    CAS  Article  Google Scholar 

  2. 2.

    Feng, L., El-Ganainy, R. & Ge, L. Non-Hermitian photonics based on parity-time symmetry. Nat. Photon. 11, 752–762 (2017).

    ADS  CAS  Article  Google Scholar 

  3. 3.

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

    MathSciNet  CAS  Article  Google Scholar 

  4. 4.

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

    ADS  CAS  Article  Google Scholar 

  5. 5.

    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 

  6. 6.

    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 

  7. 7.

    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 

  8. 8.

    Vollmer, F. & Yang, L. Review label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices. Nanophotonics 1, 267–291 (2012).

    ADS  CAS  Article  Google Scholar 

  9. 9.

    Zhu, J. et al. On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator. Nat. Photon. 4, 46–49 (2010); corrigendum 4, 122 (2010).

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Xu, X., Jiang, X., Zhao, G. & Yang, L. Phone-sized whispering-gallery microresonator sensing system. Opt. Express 24, 25905–25910 (2016).

    ADS  CAS  Article  Google Scholar 

  11. 11.

    Li, J., Suh, M.-G. & Vahala, K. J. Microresonator Brillouin gyroscope. Optica 4, 346–348 (2017).

    ADS  Article  Google Scholar 

  12. 12.

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

    ADS  Article  Google Scholar 

  13. 13.

    Maayani, S. et al. Flying couplers above spinning resonators generate irreversible refraction. Nature 558, 569–572 (2018).

    ADS  CAS  Article  Google Scholar 

  14. 14.

    Khial, P. P., White, A. D. & Hajimiri, A. Nanophotonic optical gyroscope with reciprocal sensitivity enhancement. Nat. Photon. 12, 671–675 (2018); publisher correction 12, 714 (2018); author correction 13, 220 (2019).

    ADS  CAS  Article  Google Scholar 

  15. 15.

    Gundavarapu, S. et al. Sub-Hertz fundamental linewidth photonic integrated Brillouin laser. Nat. Photon. 13, 60–67 (2019).

    ADS  CAS  Article  Google Scholar 

  16. 16.

    Wiersig, J. Sensors operating at exceptional points: general theory. Phys. Rev. A 93, 033809 (2016).

    ADS  Article  Google Scholar 

  17. 17.

    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 

  18. 18.

    Liu, Z.-P. et al. Metrology with PT-symmetric cavities: enhanced sensitivity near the PT-phase transition. Phys. Rev. Lett. 117, 110802 (2016).

    ADS  Article  Google Scholar 

  19. 19.

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

    ADS  CAS  Article  Google Scholar 

  20. 20.

    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 

  21. 21.

    Li, J., Lee, H., Chen, T. & Vahala, K. J. Characterization of a high coherence, Brillouin microcavity laser on silicon. Opt. Express 20, 20170–20180 (2012).

    ADS  CAS  Article  Google Scholar 

  22. 22.

    Lee, H. et al. Chemically etched ultrahigh-Q wedgeresonator on a silicon chip. Nat. Photon. 6, 369–373 (2012).

    ADS  CAS  Article  Google Scholar 

  23. 23.

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

    ADS  Article  Google Scholar 

  24. 24.

    Cai, M., Painter, O. & Vahala, K. J. Observation of critical coupling in a fiber taper to a silica-microsphere whisperinggallery mode system. Phys. Rev. Lett. 85, 74–77 (2000).

    ADS  CAS  Article  Google Scholar 

  25. 25.

    Spillane, S. M., Kippenberg, T. J., Painter, O. J. & Vahala, K. J. Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics. Phys. Rev. Lett. 91, 043902 (2003).

    ADS  CAS  Article  Google Scholar 

  26. 26.

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

    ADS  CAS  Article  Google Scholar 

  27. 27.

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

    ADS  CAS  Article  Google Scholar 

  28. 28.

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

    ADS  Article  Google Scholar 

  29. 29.

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

    ADS  CAS  Article  Google Scholar 

  30. 30.

    Chen, C., Jin, L. & Liu, R.-B. Sensitivity of parameter estimation near the exceptional point of a non-hermitian system. New J. Phys. 21, 083002 (2019).

    ADS  Article  Google Scholar 

  31. 31.

    Pick, A. et al. General theory of spontaneous emission near exceptional points. Opt. Express 25, 12325–12348 (2017).

    ADS  Article  Google Scholar 

  32. 32.

    Wang, H., Lai, Y.-H., Yuan, Z., Suh, M.-G. & Vahala, K. J. Petermann-factor limited sensing near an exceptional point. Preprint at https://arxiv.org/abs/1911.05191 (2019).

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Acknowledgements

We thank M. Khajavikhan, D. Christodoulides, O. Peleg and B. Loevsky for discussions during the preparation of this manuscript. We also thank B. Shen, C. Bao and Q. Yang for technical support. Y.-K.L. thanks the Caltech SURF programme for financial support. This project was supported by the Defense Advanced Research Projects Agency (DARPA) under the PRIGM:AIMS programme through SPAWAR (grant number N66001-16-1-4046) and the Kavli Nanoscience Institute.

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Authors

Contributions

Y.-K.L., Y.-H.L., M.-G.S. and K.V. conceived the idea of EP enhancement in the offset-counter-pumped SBL gyroscope. Y.-K.L., Y.-H.L. and K.V. constructed the theoretical model. M.-G.S. fabricated the ultrahigh-Q silica microresonator and helped Y.-H.L. with the packaging. Y.-H.L. and Y.-K.L. performed the experiment. Z.Y. assisted with the gyroscope sensitivity measurements. All authors analysed the data and wrote the manuscript.

Corresponding author

Correspondence to Kerry Vahala.

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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.

Extended data figures and tables

Extended Data Fig. 1 Diagram of the counter-pumped SBL gyroscope.

See Methods for operational description. PDH, Pound–Drever–Hall lock; ECDL, external-cavity diode laser; EDFA, erbium-doped fibre amplifier; PM, phase modulator; PD, photodetector; ESA, electrical spectrum analyser; FC, frequency counter; PI, proportional-integral servo; RF: radio frequency; f1 (f2): modulation frequency of AOM1 (AOM2); fPDH, phase-modulation frequency of the PDH loop.

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Supplementary Information

This file contains Supplementary Sections 1-4.

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Lai, YH., Lu, YK., Suh, MG. et al. Observation of the exceptional-point-enhanced Sagnac effect. Nature 576, 65–69 (2019). https://doi.org/10.1038/s41586-019-1777-z

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