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Bulletin of the American Physical Society

Initial Phase Dependence of the Sagnac Effect for Matter Waves

Martin C. Kandes, M. W. J. Bromley, R. Carretero-González

Published Jun 6, 2017• 0 citations
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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.
A gyroscope based on Sagnac interferometer measures the rotation rate relative to an inertial frame of reference. Sagnac effect originally has been derived and experimentally demonstrated with optical waves. Later, matter wave based Sagnac interferometers were developed due to inherent sensitivity over a photon based system. However in any interferometer whether it is photon or matter wave based the resultant phase shift due to counter-rotating waves is independent of the wave velocity. Here we show that one can have a larger phase shift with slower matter waves using Aharonov-Bohm effect: the phase difference of the counter propagating waves is proportional to the inverse square of the particle velocity.