Atom interferometry is of considerable interest in part because of the ability to interferometrically detect inertial rotations via the Sagnac effect with a potential sensitivity 1010 greater than optical gyroscopes. It has been shown recently that a coherently coupled array of identical interferometers can significantly enhance the sensitivity to rotations due to the appearance of transmission bands as a function of the inertial rotation rate Ω. Here we consider phase coherent transport of atomic matter waves in a chain of ring interferometers with a single occupied transverse mode in the presence of a rotation, Ω, and study the effect of variations in the size of the rings. We show that for randomly sized rings, the entire array functions as a highly sensitive Sagnac interferometer provided the level of random size fluctuations does not exceed a few per cent of the mean size. We also analyse how the use of individual defect states and controlled variations of the sizes in the array can be used to further enhance the sensitivity by creating narrow transmission resonances inside of a zero transmission gap.
The utilization of atom interferometry for gyroscopes is of considerable interest because the detection of inertial rotations via the Sagnac effect has a potential
1010 greater sensitivity than optical gyroscopes. Here we analyze, in the presence of a rotation $\ensuremath{\Omega}$, phase-coherent transport of atomic matter waves in a one-dimensional chain of
N ring interferometers in which the sizes of the rings are chirped symmetrically about the center ring. The gyroscope scale factor of the area-chirped array for $N\ensuremath{\lesssim}10$ is several orders of magnitude larger than that for the unchirped array, which itself is larger than the scale factor of a Mach-Zehnder interferometer with the same enclosed area. This enhancement is achieved with total enclosed areas that are larger or smaller than that of the unchirped array by less than 25
. As such, the area chirp achieves rotation sensitivities with $N\ensuremath{\lesssim}10$ interferometers that would normally require $N\ensuremath{\gg}100$ rings of identical sizes.