A large-momentum-transfer matter-wave interferometer to measure the effect of gravity on positronium

This paper reports the study of a new interferometric configuration to measure the effect of gravity on positronium. A Mach-Zehnder matter-wave interferometer has been designed to operate with single-photon transitions and to transfer high momentum to a 200 eV positronium beam. The work shows the results and methods used to simulate the interferometer and estimate the operating parameters and the time needed to perform the experiment. It has been estimated that within less than one year, the acquisition time is sufficient to achieve a 10\% accuracy level in measuring positronium gravitational acceleration, even with a poorly collimated beam, which is significant for theoretical models describing matter-antimatter symmetry. These results pave the way for single photon transition large momentum transfer interferometry with fast atomic beams, which is particularly useful for studies with antimatter and unstable atoms.