Gravitational quantum states of Antihydrogen

We present a theoretical study of the motion of the antihydrogen atom ((H) over bar) in the gravitational field of Earth above a material surface. We predict that the (H) over bar atom, falling in the gravitational field of Earth above a material surface, would settle into long-lived quantum states. We point out a method of measuring the difference in the energy of (H) over bar in such states. The method allows for spectroscopy of gravitational levels based on atom-interferometric principles. We analyze the general feasibility of performing experiments of this kind. We point out that such experiments provide a method of measuring the gravitational force (Mg) acting on (H) over bar and that they might be of interest in the context of testing the weak equivalence principle for antimatter.