Electron Sagnac gyroscope in an array of mesoscopic quantum rings

The Sagnac effect is an important phase coherent effect in optical and atom interferometers where rotations with respect to an inertial frame are measured in the interference pattern. We analyze the Sagnac effect in a serial array of mesoscopic ring shaped electron interferometers comprised of rings with half-circumferences comparable to the mean free path. The entire array is, however, much larger than the phase coherence length. Phase coherent transport at the level of individual rings leads to a measurable Sagnac effect in the conductance of the chain. We use the signal to noise ratio (SNR) to determine the number of rings needed to measure a desired rotation rate.