  We theoretically propose a scheme to realize rotation sensing based on two
coupled whispering-gallery-mode resonators with loss and gain. We consider that
the active resonator with gain is rotated while the passive one with loss is
stationary. The rotation will induce Sagnac effect and we show that the
eigenfrequencies of the supermodes are sensitive to the Sagnac-Fizeau shift.
Therefore, we can measure the average photon number in the steady state or the
fluctuation spectrum of the output fields to detect the angular velocity of the
rotation. We hope that our investigation will be useful in the design of
quantum gyroscope based on spinning resonators.
