Sagnac Rotational Phase Shifts in a Mesoscopic Electron Interferometer with Spin-Orbit Interactions

The Sagnac effect is an important phase coherent effect in optical and atom interferometers where rotations of the interferometer with respect to an inertial reference frame result in a shift in the interference pattern proportional to the rotation rate. Here we analyze for the first time the Sagnac effect in a mesoscopic semiconductor electron interferometer. We include in our analysis Rashba spin-orbit interactions in the ring. Our results indicate that spin-orbit interactions increase the rotation induced phase shift. We discuss the potential experimental observability of the Sagnac phase shift in such mesoscopic systems.