H\"ansch-Couillaud locking of a large Sagnac interferometer: advancing below the flicker floor

Large Sagnac interferometers in the form of active ring lasers have emerged as unique rotation sensors in the geosciences, where their sensitivity allows to detect geodetic and seismological signals. The passive laser gyroscope variant, however, is still at a stage of development, and thus far, only the Pound-Drever-Hall frequency stabilization technique has been explored, a method limited by residual amplitude modulation. Here, as an alternative method, we present the first H\"ansch-Couillaud locked passive laser gyroscope. We find that this method is limited by flicker noise, and we introduce a cost-effective lock-in scheme to overcome this limitation. We achieve a sensitivity of 3.1 nrad/s, corresponding to a fraction of $7.7\cdot 10^{-5}$ in the Earth's rotation rate.