  We study an interferometric approach to measure gravitational mass of
antihydrogen. The method consists of preparing a coherent superposition of
antihydrogen quantum state localized near a material surface in the
gravitational field of the Earth, and then observing the time distribution of
annihilation events followed after the free fall of an initially prepared
superposition from a given height to the detector plate. We show that a
corresponding time distribution is related to the momentum distribution in the
initial state that allows its precise measurement. This approach is combined
with a method of production of a coherent superposition of gravitational states
by inducing a resonant transition using oscillating gradient magnetic field. We
estimate an accuracy of measuring the gravitational mass of antihydrogen atom
which could be deduced from such a measurement.
