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Different experiments are ongoing to measure the effect of gravity on coldneutral antimatter atoms such as positronium, muonium and antihydrogen. Amongthose, the project GBAR in CERN aims to measure precisely the gravitationalfall of ultracold antihydrogen atoms. In the ultracold regime, the interactionof antihydrogen atoms with a surface is governed by the phenomenon of quantumreflection which results in bouncing of antihydrogen atoms on matter surfaces.This allows the application of a filtering scheme to increase the precision ofthe free fall measurement. In the ultimate limit of smallest verticalvelocities, antihydrogen atoms are settled in gravitational quantum states inclose analogy to ultracold neutrons (UCNs). Positronium is another neutralsystem involving antimatter for which free fall under gravity is currentlybeing investigated at UCL. Building on the experimental techniques underdevelopment for the free fall measurement, gravitational quantum states couldalso be observed in positronium. In this contribution, we review the status ofthe ongoing experiments and discuss the prospects of observing gravitationalquantum states of antimatter and their implications.

Prospects for studies of the free fall and gravitational quantum states of antimatter