  Using an atom-cavity platform, we propose to combine the effective gauge
phase of rotated neutral atoms and the superradiant phase transition to build a
highly sensitive and fast quantum rotation sensor. The atoms in a
well-controlled array of Bose-Einstein condensates are coupled to a single
light mode of an optical cavity. The photon emission from the cavity indicates
changes in the rotation frequency in real time, which is crucial for inertial
navigation. We derive an analytical expression for the phase boundaries and use
a semi-classical method to map out the phase diagram numerically, which
provides the dependence of the photon emission on the rotation. We further
suggest to operate the sensor with a bias rotation, and to enlarge the enclosed
area, to enhance the sensitivity of the sensor.
