Quantum metrology in the Kerr metric

A surprising feature of the Kerr metric is the anisotropy of the speed of light. The angular momentum of a rotating massive object causes co- and counterpropagating light paths to move at faster and slower velocities, respectively, as determined by a far-away clock. Based on this effect we derive the ultimate quantum limits for the measurement of the Kerr rotation parameter a using an interferometric setup. As a possible implementation, we propose a Mach-Zehnder interferometer to measure the "one-way height differential" time effect. We isolate the effect by calibrating to a dark port and rotating the interferometer such that only the direction-dependent Kerr-metric-induced phase term remains. We transform to the zero angular momentum observer (ZAMO) flat metric where the observer sees c=1. We use this metric and the Lorentz transformations to calculate the same Kerr phase shift. We then consider nonstationary observers moving with the planet's rotation, and we find a method for canceling the additional phase from the classical relative motion, thus leaving only the curvature-induced phase.