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.
Highlights
Gravitational properties of antimatter have never been measured directly
As it is not experimentally feasible to further cool down the ions to reach the optimum size of the initial cloud, we propose in this paper to select the initial vertical velocity of the atoms
For our proposal to be useful as an improved option of the GBAR measurement, one must ensure that there are no large systematic uncertainties which could contribute at a level comparable to the estimated statistical uncertainty of 10−3
Summary
A promising experimental method to do so consists in producing sufficiently cold antihydrogen atoms (H) and timing their free fall in the Earth’s gravity field. This approach is being pursued by AEGIS [1], ATHENA-ALPHA [2], ATRAP [3] and GBAR [4] collaborations. The precision of this measurement depends crucially on the dispersion of vertical velocities before the free fall, which corresponds to the residual kinetic energy of the atoms after the cooling process. The atomic recoil in the photo-detachment process induces an additional velocity dispersion which is discussed in the last section on systematic effects
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