Towards measuring gravity on neutral antimatter

One of the antimatter community current biggest efforts is to measure gravity on a neutral antimatter system, towards a first test of Equivalence Principle - a cornerstone of General Relativity. Any deviation from the expected identical behaviour with respect to normal matter would be an indication of new physics. This thesis explores the possibility to measure gravity with cold antihydrogen (Hbar) produced with a novel pulsed scheme based on a charge-exchange reaction between antiprotons and Rydberg positronium (Ps). Hbar and Ps are currently the only neutral antimatter systems available in quantities at low temperatures, and both are being considered for measuring gravity. Several results towards producing pulsed charge-exchange Hbar were obtained in the context of the AEgIS experiment. Positronium was produced with 35% effciency in a dedicated setup, where spectroscopy of the 13S - 33P transition and subsequent excitation to Rydberg levels were performed with ~ 15% effciency (bandwidth limited). Ps was produced also in the cryogenic Hbar production region of AEgIS (with ~25% effciency), where ~10^5 antiprotons were also stored for minutes after capture, cooling, radial compression and transfer. An estimate showed that 3-40 Hbar atoms per measurement run could be formed in the present setup. The experimental work motivated two detailed theoretical studies. A numerical code for calculating Rydberg Ps energy levels and optical spectra in arbitrary (strong) external fields, based on a non-perturbative approach, was developed. Results well reproduced high-resolution spectroscopic data from experiments, and also demonstrated the feasibility of measuring both Ps axial and transverse velocity components using only transverse laser probes. A novel numerical method for calculating single-species non-neutral plasma equilibria in cylindrical trap at low T was also developed, showing higher robustness and faster convergence to solution (T^-1) than currently available methods (T^-2). Finally, the combined availability of the intense Ps source and the 13S - 33P laser made possible to observe the 23S metastable state of positronium by optical decay from 33P, with a measured effciency of ~1%. This result represents a first step towards a gravity measurement on metastable 23S positronium.