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Observation of the exceptional-point-enhanced Sagnac effect


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.


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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 and Affiliations



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).

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