The Gbar project, or how does antimatter fall?

The Einstein classical Weak Equivalence Principle states that the trajectory of a particle is independent of its composition and internal structure when it is only submitted to gravitational forces. This fundamental principle has never been directly tested with antimatter. However, theoretical models such as supergravity may contain components inducing repulsive gravity, thus violating this principle. The GBAR project (Gravitational Behaviour of Antihydrogen at Rest) proposes to measure the free fall acceleration of ultracold neutral antihydrogen atoms in the terrestrial gravitational field. The experiment consists in preparing antihydrogen ions (one antiproton and two positrons) and sympathetically cool them with Be+ ions to a few 10 mu K. The ultracold ions will then be photoionized just above threshold, and the free-fall time over a known distance measured. In this work, the GBAR project is described as well as possible improvements that use quantum reflection of antihydrogen on surfaces to use quantum methods of measurements.