Testing the weak equivalence principle with positronium by Rydberg-atom interferometry

We describe an experimental scheme wherein phase shifts induced by the gravitational field of the Earth on atoms in superpositions of Rydberg states with large static electric dipole moments can be observed by matter-wave interferometry. Such measurements, performed using positronium (Ps) atoms would constitute a test of the weak equivalence principle for a purely leptonic matter-antimatter system. Using realistic experimental parameters, obtained from measured data, we estimate that this approach could make it possible to measure the gravitational acceleration of Ps with a precision on the order of 10%.