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.


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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.

Correspondence to Mercedeh Khajavikhan.

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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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