  In the GBAR experiment, cold antihydrogen atoms will be left to fall on an
annihilation plate with the aim of measuring the gravitational acceleration of
antimatter. Here, we study the quantum reflection of these antiatoms due to the
Casimir-Polder potential above the plate. We give realistic estimates of the
potential and quantum reflection amplitudes, taking into account the
specificities of antihydrogen and the optical properties of the plate. We find
that quantum reflection is enhanced for weaker potentials, for example above
thin slabs, graphene and nanoporous media.
