Semiclassical Phase Analysis for a Trapped-Atom Sagnac Interferometer

TL;DR

This paper analyzes how imperfections in a trapped-atom Sagnac interferometer affect phase shifts, providing theoretical insights and experimental measurements to improve rotation sensing accuracy.

Contribution

It offers a comprehensive theoretical analysis of phase shifts due to anharmonic and other perturbations in a trapped-atom Sagnac interferometer, including experimental validation.

Findings

Phase shifts are mainly second order in perturbations.

Sensitive parameters must be controlled at 10^{-5} level.

Perfect cylindrical symmetry suppresses leading-order perturbations.

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.