Shaping the distribution of vertical velocities of antihydrogen in GBAR

Dufour, G.; Reynaud, S.; Voronin, A.Yu.; Lambrecht, A.; Debu, P.; Nesvizhevsky, V.V.

doi:10.1140/epjc/s10052-014-2731-8

Article
Report number	arXiv:1312.5534
Title	Shaping the distribution of vertical velocities of antihydrogen in GBAR
Author(s)	Dufour, G. (Paris, Lab. Kastler Brossel) ; Debu, P. (IRFU, Saclay) ; Lambrecht, A. (Paris, Lab. Kastler Brossel) ; Nesvizhevsky, V.V. (Laue-Langevin Inst.) ; Reynaud, S. (Paris, Lab. Kastler Brossel) ; Voronin, A.Yu. (Lebedev Inst.)
Publication	2014-01-30
Imprint	19 Dec 2013
Number of pages	21
In:	Eur. Phys. J. C 74 (2014) 2731
DOI	10.1140/epjc/s10052-014-2731-8
Subject category	physics.ins-det ; Detectors and Experimental Techniques ; quant-ph ; General Theoretical Physics ; physics.atom-ph ; Other Fields of Physics
Accelerator/Facility, Experiment	CERN AD ; GBAR AD-7
Abstract	GBAR is a project aiming at measuring the free fall acceleration of gravity for antimatter, namely antihydrogen atoms ($\overline{\mathrm{H}}$). Precision of this timing experiment depends crucially on the dispersion of initial vertical velocities of the atoms as well as on the reliable control of their distribution. We propose to use a new method for shaping the distribution of vertical velocities of $\overline{\mathrm{H}}$, which improves these factors simultaneously. The method is based on quantum reflection of elastically and specularly bouncing $\overline{\mathrm{H}}$ with small initial vertical velocity on a bottom mirror disk, and absorption of atoms with large initial vertical velocities on a top rough disk. We estimate statistical and systematic uncertainties, and show that the accuracy for measuring the free fall acceleration $\overline{g}$ of $\overline{\mathrm{H}}$ could be pushed below $10^{-3}$ under realistic experimental conditions.
Copyright/License	CC-BY-3.0

$A scheme of principle of the proposed shaping device: an $\Hb$ atom is released from the Paul trap (central spot) and it bounces a few times on the mirror surface of the bottom disk (arrows); if it scatters on the rough top surface, it annihilates (lightnings); otherwise, it escapes from the aperture between the two disks, and falls to the detection plate where it annihilates (lightning on the detection plate). $R$ is the radius of the bottom and top disks, $r$ is the radius of central openings in the disks, $h$ is the distance between the top surface of the bottom disk and the bottom surface of the top disk, $H$ is the distance between the top of the detection plate and the top of the bottom disk, $L$ is the horizontal distance between the initial spot and the detection point.$ $The distribution of annihilation times of $\Hb$ falling from the height $H=30$~cm; in the upper plot, the initial state is a Gaussian of width $\zeta=70$~nm, a typical value expected in the GBAR experiment; in the lower plot, it is a Gaussian with the optimal width $\zeta_{opt}=88$~$\mu$m. For comparison, the time scale is the same on both graphs. A zoom on the peak is shown in the inset for the lower plot.$ $The distribution of annihilation times of $\Hb$ falling from the height $H=30$~cm; in the upper plot, the initial state is a Gaussian of width $\zeta=70$~nm, a typical value expected in the GBAR experiment; in the lower plot, it is a Gaussian with the optimal width $\zeta_{opt}=88$~$\mu$m. For comparison, the time scale is the same on both graphs. A zoom on the peak is shown in the inset for the lower plot.$ Show more plots

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