Shaping the distribution of vertical velocities of antihydrogen in GBAR

GBAR is a project aiming at measuring the free-fall acceleration of gravity for antimatter, namely antihydrogen atoms ((H) over bar). The 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 the vertical velocities of (H) over bar, which improves these factors simultaneously. The method is based on quantum reflection of elastically and specularly bouncing (H) over bar 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 we show that the accuracy for measuring the free fall acceleration (g) over bar of (H) over bar could be pushed below 10(-3) under realistic experimental conditions.