Frequency noise of laser gyros

Laser gyros are powerful tools to test the predictions of the general theory of relativity. The precision of a measurement of the rotation rate with a laser gyro is limited by the frequency noise of the beat between two counterpropagating modes of a ring laser. The frequency noise of a single mode of a laser is limited by quantum mechanical constraints because it is related to the maximum precision with which the phase of a coherent state can be measured. If two modes are uncorrelated, the variance of the fluctuations of the difference of the their frequencies is the sum of the variance of the frequency noise of the two modes. If two modes are correlated, this result does not hold any longer. In this paper, we show that there are mechanisms in a laser gyro that are capable to dynamically lock the two modes together without forcing the two modes to the same frequency. The lock of modes decouples the noise of the beat note from the frequency noise of the individual modes, and allows the realization of sub-shot noise laser gyros. These mechanism may explain the recent observation of sub-shot noise performance of the GINGERino laser gyro recently reported in the literature.