We theoretically study both the technical and the fundamental quantum limitations of the sensitivity of a resonant optical gyroscope based on a high finesse optical cavity. We show that the quantum back action associated with the resonantly enhanced optical cross and self-phase modulation results in the nonlinear optics-mediated standard quantum limit (SQL) of the angle random walk of the gyroscope. We also found that the measurement sensitivity of a generic optical gyroscope is fundamentally limited due to the opto-mechanical properties of the device. Ponderomotive action of the light interrogating the gyroscope cavity leads to the opto-mechanical SQL of the rotation angle detection. The uncorrelated quantum fluctuations of power of clockwise and counterclockwise light waves result in optical power-dependent uncertainty of the angular gyroscope position.

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A. B. Matsko, S. P. Vyatchanin, A. A. Savchenkov, and S. Williams, "Quantum limitations and back action evading measurements in classical force and rotation detection," Proc. SPIE 10934, Optical, Opto-Atomic, and Entanglement-Enhanced Precision Metrology, 109340V (Presented at SPIE OPTO: February 03, 2019; Published: 1 March 2019); https://doi.org/10.1117/12.2515797.