Optimization of the atom interferometer phase produced by the set of cylindrical source masses to measure the Newtonian gravity constant

TL;DR

This paper derives an analytical model for the gravitational field of cylinders and optimizes atom interferometer configurations to measure the Newtonian gravitational constant with high precision, accounting for systematic errors and Earth's gravity effects.

Contribution

It provides a new analytical expression for cylindrical mass gravitational fields and optimizes atom interferometer parameters to improve measurement accuracy of G.

Findings

Achieved predicted measurement accuracy of 10^-4 and 2*10^-5 for different cylinder sets.

Identified conditions under which systematic errors due to cloud size and temperature vanish.

Proposed a gravity-gradient elimination technique to enhance measurement precision.

Abstract

An analytical expression for the gravitational field of a homogeneous cylinder is derived. The phase of the atom interferometer produced by the gravity field of the set of cylinders has been calculated. The optimal values of the initial positions and velocities of atomic clouds were obtained. It is shown that at equal sizes of the atomic cloud in the vertical and transverse directions, as well as at equal atomic vertical and transverse temperatures, systematic errors due to the finite size and temperature of the cloud disappear. To overcome the influence of the Earth gravitational field on the accuracy of the phase double difference measurement, it is proposed to use the technique of eliminating gravity-gradient terms. After eliminating, one can use extreme values of the atomic positions and velocities. Nonlinear dependences of the phase on the uncertainties of atomic positions and velocities near those extreme values required us to modify the expression for the standard phase deviation. Moreover, such dependences lead to a phase shift, which was also calculated. The relative accuracy of measurements of Newtonian gravitational constant 10^-4 and 2*10^-5 is predicted for sets of 24 and 630 cylinders, respectively.