Analysis of the timing of freely falling antihydrogen

TL;DR

This paper assesses the precision of measuring antihydrogen free fall acceleration in the GBAR experiment, highlighting initial velocity dispersion as the main uncertainty source rather than photodetachment recoil.

Contribution

It provides a detailed analysis showing that initial velocity dispersion dominates measurement uncertainty, simplifying experimental constraints on laser parameters.

Findings

Initial velocity dispersion is the main source of uncertainty.

Photodetachment recoil is less limiting than previously thought.

The results facilitate more flexible laser parameter choices.

Abstract

We evaluate the accuracy to be expected for the measurement of free fall acceleration of antihydrogen in the GBAR experiment, accounting for the recoil transferred in the photodetachment process. We show that the uncertainty on the measurement of gravity comes mainly from the initial velocity dispersion in the ion trap so that the photodetachment recoil is not the limiting factor to the precision as a naive analysis would suggest. This result will ease the constraints on the choice of the photodetachment laser parameters.