Phase-Shift Plateaus in the Sagnac Effect for Matter Waves

We simulate ultracold Sagnac atom interferometers using quantum-mechanical matter wavepackets, e.g. Bose-Einstein condensates, that counter-propagate within a rotating ring-trap. We find that the accumulation of the relative phase difference between wavepackets, i.e. the matter wave Sagnac effect, is manifested as discrete phase jumps. These plateaus result from three effects; that the atoms should be initially trapped at rest with respect to the rotating frame, that they counter-propagate with the same group velocities in the rotating frame, and that the imaging is performed in the rotating frame. We show that the plateaus persist in the presence of nonlinear atom-atom interactions, and in atoms undergoing various rotations, and thus will occur during matter wavepacket experiments. We also introduce the simplest possible Sagnac atom interferometry scheme which relies on wavepacket dispersion around a ring-trap.