Geometric phase shift sensitivity in an area chirped array of atom interferometers

Abstract

Measuring geometric phase shifts has various applications in both quantum and classical interferometry such as measuring acceleration, distances, rotation and magnetic flux. Theoretical analysis of coupled ring arrays has been shown to be a promising design for creating small inertial rotation sensors on atom chips. In this paper we build on the theoretical models of transmission of matter waves through an area chirped array of ring interferometers to determine phase regions of the transmission that exhibit high sensitivity to geometric phase shifts,these regions are indicated by sharp transmission resonances. We calculate the slopes of transmission resonances for a range of values for two parameters, the chirp factor γ and the product of the wave number and ring circumference kL, we look at the behavior of the slopes of these transmission resonances for defined ranges of kL and γ to see in search of transmission resonances with extreme slopes. We find transmission resonances with sensitivities to geometric phase shifts that exceed those found in previous models of area chirped arrays by several orders of magnitude. The area chirp is applied such that the geometric phase shifts (θGP) in each ring of the array can be expressed in terms of the geometric phase shift in the reference ring of the array, this enables the transmission function T(θGP) to be calculated in terms of the phase shift of a single ring. We investigate T(θGP) for various ring sizes, wave numbers, and chirp factor and look for values of these parameters that lead to sharp transmission resonances in T(θGP). We calculate the sensitivities of rotation via the Sagnac effect and magnetic flux via Aharonov Bohm effect based on the sensitivity of the transmission resonances found in our transmission functions.