Optimization and error model for atom interferometry technique to measure Newtonian gravitational constant

TL;DR

This paper develops an optimization and error model for atom interferometry used to measure the Newtonian gravitational constant, focusing on minimizing phase errors caused by proof mass and atomic variable deviations.

Contribution

It introduces a method to find extrema of phase contribution in atom interferometers with a 100kg tungsten proof mass, reducing positioning requirements significantly.

Findings

Identified extremal atomic variable values to minimize phase errors.

Quantified response variations due to small deviations in atomic and proof mass parameters.

Reduced atom positioning accuracy requirements by two orders of magnitude.

Abstract

Considered contribution to the phase of the atom interferometer caused by the gravity field of the massive proof mass. Demonstrated the method of finding the extrema of this contribution for 100kg Tungsten proof mass of the specific shape and specific parameters of $^{133}Cs$ atom interferometers. Calculated variations of the double difference response under the small deviations of atomic and proof mass variables. The choice of the extremal values of the atomic variables allows one to release requirements for atom positioning on 2 orders of magnitude.