Quantum ballistic experiment on antihydrogen fall

We propose an approach to measuring gravitational mass of antihydrogen ($\overline{H}$) based on interferometry of time distribution of free-fall events of antiatoms. Our method consists of preparing a coherent superposition of quantum states of $\overline{H}$ localized near a material surface in the gravitational field of the Earth, and then observing the time distribution of annihilation events after the free-fall of the initially prepared superposition from a given height to a detector plate. We show that the time distribution of interest is mapped to a precisely predictable velocity distribution of the initial wave packet. This approach is combined with production of a coherent superposition of gravitational states by inducing a resonant transition using an oscillating gradient magnetic field. We show that the relative accuracy of measuring the $\overline{H}$ atom gravitational mass can be achieved with this approach is 10⁻⁴, with 10³ antiatoms settled in lowest gravitational states. (paper)