Interaction of ultracold antihydrogen with a conducting wall

We investigate the interaction of ultracold antihydrogen with a conducting surface, focusing on the phenomenon of quantum reflection. We calculate the reflection probability as a function of incident atom energy. We find that, for ground-state (H) over bar atoms (with T < 10(-5) K), the probability of reflection is R similar or equal to 1-kb, where k is the momentum of the atom and b=2174.0 a.u. is a constant determined solely by the van der Waals-Casimir tail of the atom-wall interaction. We show that quantum reflection, which suppresses the direct contact of ultracold atoms with the surface, allows for the possibility of confinement and storage of sufficiently cold antihydrogen atoms. We calculate the lifetime of (H) over bar atoms enclosed in between solid walls. We develop a theory of (H) over bar in a waveguide and propose some applications, notably the measurement of retardation corrections in the long-range component of the antiatom-wall potential. We demonstrate the existence of quantized states for antihydrogen atoms falling onto conducting surface in the gravitational field of Earth. We calculate the lifetime of ultracold (H) over bar in its lowest gravitational state and obtain tau=(Mgb/2h)(-1)similar or equal to 0.1 s, where Mg is a gravitational force acting on the antiatom. We propose that measurement of this lifetime may provide a new test for the gravitational properties of antimatter.