Standard quantum limit of sensitivity of an optical gyroscope

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We find that the measurement sensitivity of an optical integrating gyroscope is fundamentally limited due to ponderomotive action of the light leading to the standard quantum limit of the rotation angle detection. The uncorrelated quantum fluctuations of power of clockwise and counterclockwise electromagnetic waves result in optical power-dependent uncertainty of the angular gyroscope position. We also show that, on the other hand, a quantum backaction evading measurement of the angular momentum of a gyroscope becomes feasible if the proper measurement strategy is selected. The angle is perturbed in this case. This observation hints at the fundamental inequivalence of integrating and rate gyroscopes.