John Toland

Ultra-sensitive chip scale Sagnac gyroscope based on periodically modulated coupling of a coupled resonator optical waveguide

We analyze the sensitivity to inertial rotations Ω of a micron scale integrated gyroscope consisting of a coupled resonator optical waveguide (CROW). We show here that by periodic modulation of the evanescent coupling between resonators, the sensitivity to rotations can be enhanced by a factor up to 10(9) in comparison to a conventional CROW with uniform coupling between resonators. Moreover, the overall shape of the transmission through this CROW superlattice is qualitatively changed resulting in a single sharp transmission resonance located at Ω = 0s-1 instead of a broad transmission band. The modulated coupling therefore allows the CROW gyroscope to operate without phase biasing and with sensitivities suitable for inertial navigation even with the inclusion of resonator losses.

Chirped area coupled resonator optical waveguide gyroscope

We study the transmission of an optical field through a rotating coupled resonator optical waveguide (CROW) in which the size of the ring resonators changes from one ring to the next. We focus on symmetric integer wavelength chirps of the circumference of the rings relative to the central ring in the array. The transfer matrix method is used to obtain the transmission as a function of the inertial rotation rate Ω resulting from the Sagnac effect. Chirping increases the slope of the oscillations in the transmission as a function of Ω, which can be exploited to further enhance the rotation sensitivity beyond that of a CROW with uniform resonators.

Atom gyroscope with disordered arrays of quantum rings

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.

Sagnac effect in a chain of mesoscopic quantum rings

The ability to interferometrically detect inertial rotations via the Sagnac effect has been a strong stimulus for the development of atom interferometry because of the potential 10{sup 10} enhancement of the rotational phase shift in comparison to optical Sagnac gyroscopes. Here we analyze ballistic transport of matter waves in a one-dimensional chain of N coherently coupled quantum rings in the presence of a rotation of angular frequency {omega}. We show that the transmission probability, T, exhibits zero transmission stop gaps as a function of the rotation rate interspersed with regions of rapidly oscillating finite transmission. With increasing N, the transition from zero transmission to the oscillatory regime becomes an increasingly sharp function of {omega} with a slope {partial_derivative}T/{partial_derivative}{omega}{approx}N{sup 2}. The steepness of this slope dramatically enhances the response to rotations in comparison to conventional single ring interferometers such as the Mach-Zehnder interferometer and leads to a phase sensitivity well below the quantum shot-noise limit typical of atom interferometers.