Semiclassical Phase Analysis for a Trapped-Atom Sagnac Interferometer

Zhe Luo,C A Sackett,E R Moan

doi:10.3390/atoms9020021

Abstract

A Sagnac atom interferometer can be constructed using a Bose–Einstein condensate trapped in a cylindrically symmetric harmonic potential. Using the Bragg interaction with a set of laser beams, the atoms can be launched into circular orbits, with two counterpropagating interferometers allowing many sources of common-mode noise to be excluded. In a perfectly symmetric and harmonic potential, the interferometer output would depend only on the rotation rate of the apparatus. However, deviations from the ideal case can lead to spurious phase shifts. These phase shifts have been theoretically analyzed for anharmonic perturbations up to quartic in the confining potential, as well as angular deviations of the laser beams, timing deviations of the laser pulses, and motional excitations of the initial condensate. Analytical and numerical results show the leading effects of the perturbations to be second order. The scaling of the phase shifts with the number of orbits and the trap axial frequency ratio are determined. The results indicate that sensitive parameters should be controlled at the 10−5 level to accommodate a rotation sensing accuracy of 10−9 rad/s. The leading-order perturbations are suppressed in the case of perfect cylindrical symmetry, even in the presence of anharmonicity and other errors. An experimental measurement of one of the perturbation terms is presented.

Highlights

Atom interferometry is useful for many types of precision measurements [1,2,3], but one of the most attractive applications is inertial navigation [4,5]
In Ref. [14], we demonstrated a Sagnac interferometer using atoms confined in a harmonic potential, where the trap caused the atoms to move in nearly circular orbits so as to enclose an area
The methods presented here are generally useful for characterizing the performance of a trapped atom interferometer

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Atom interferometry is useful for many types of precision measurements [1,2,3], but one of the most attractive applications is inertial navigation [4,5]. In order to obtain high sensitivity, it is desirable to operate the interferometer with long measurement times T. If the confining potential is not ideal it can still impact the final phase measurement and limit the accuracy of the sensor. The interferometer visibility and enclosed area are impacted by non-idealities These are not affected by the differential measurement, so the analysis in [15] is directly applicable. We discuss the implications for experiments and compare to a measurement of the phase sensitivity for one pair of parameters

Semiclassical Phase Analysis

Harmonic Oscillator Potential

Anharmonic Potential

Implications for Experiments

Conclusions