Optical gyroscope based on the Sagnac effect have excellent potential in the application of high-sensitivity inertial rotation sensors. In this paper, we demonstrate that for an optical resonance gyroscope with normal dispersion, the measurement sensitivity can be increased by two orders of magnitude through coupling into a squeezed vacuum light, which is different from that in the classical situation. When the system is operated under critical anomalous dispersion condition, injecting a squeezed vacuum light allows the measurement sensitivity beyond the corresponding standard quantum limit by five orders of magnitude, with a minimum value of 3.8*10^-5 Hz. This work offers a promising possibility for developing optical gyroscopes that combine high sensitivity with tiny size.

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