Analysis of the timing of freely falling antihydrogen

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.

Improving the statistical analysis of anti-hydrogen free fall by using near edge events

“…The symmetrical configuration produces a simple geometry which will be more easily studied in Monte-Carlo simulations of the experiment. We will work with a horizontal polarisation of the photo-detachment laser, in order to launch the atoms preferably in the free interval between the two disks [18]. In a first part of the study we will generate random events mimicking the forthcoming experiment with a reference value g 0 = 9, 81 m/s 2 .…”

“…In a second part, we will present the statistical analysis of these events mimicking the data analysis process to be developed at a later stage for the experiment. The whole analysis will be done in a manner quite analogous to that presented in [18], with however important differences discussed now.…”

“…In [18], we detailed the calculation of the same quantity J 0 (R, T ) ignoring the presence of obstacles. In the presence of symmetrical disks in contrast, the reasoning has to consider separately the annihilation events on the surfaces of the free fall chamber, which are used for estimating g, and those on the disks, which contain essentially no information on g. Hence, we will be mainly interested in the current on the surfaces of the free fall chamber with a probability integral P c smaller than one.…”

“…The end of free fall is timed by the annihilation of H on the detection surface and the acceleration g is deduced from a statistical analysis of annihilation events. In a previous work [18], we have analysed the accuracy on g to be expected in a simple geometry for the GBAR experiment, taking into account the impact of the photo-detachment process on the initial velocity distribution and the statistics of annihilation events. We also noticed that the accuracy could be improved by considering the ceiling that intercepts some of the trajectories.…”

“…These obstacles, such as the electrodes of the ion trap, intercept some trajectories of H atoms. As for the ceiling in [18], one might think that they degrade the ac-curacy as they reduce the number of annihilation events used for the measurement. We show that the opposite happens, with an accuracy on the measurement of g improved thanks to the additional information gained from events close to the edges of the shadow of obstacles.…”