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GBAR is a project aiming at measuring the free fall acceleration of gravityfor antimatter, namely antihydrogen atoms ($\overline{\mathrm{H}}$). Precisionof this timing experiment depends crucially on the dispersion of initialvertical velocities of the atoms as well as on the reliable control of theirdistribution. We propose to use a new method for shaping the distribution ofvertical velocities of $\overline{\mathrm{H}}$, which improves these factorssimultaneously. The method is based on quantum reflection of elastically andspecularly bouncing $\overline{\mathrm{H}}$ with small initial verticalvelocity on a bottom mirror disk, and absorption of atoms with large initialvertical velocities on a top rough disk. We estimate statistical and systematicuncertainties, and show that the accuracy for measuring the free fallacceleration $\overline{g}$ of $\overline{\mathrm{H}}$ could be pushed below$10^{-3}$ under realistic experimental conditions.

Shaping the distribution of vertical velocities of antihydrogen in GBAR