  We theoretically propose a scheme to perform rotation sensing in a
Whispering-gallery-mode resonator setup. With the assistance of a large detuned
two-level atom, which induces the effective coupling between clockwise and
counterclockwise propagating modes in the resonator, we realize an effective
interferometry with SU(2) algebraic structure. By studying the quantum Fisher
information of the system, we find that the estimate accuracy for the angular
velocity of the rotation can achieve and even break the Heisenberg limit in
linear and nonlinear setup, respectively. The high performance of quantum
metrology is proved to be associated with the state compressibility during the
time evolution. We hope that our investigation will be useful in the design of
a quantum gyroscope based on spinning resonators.
