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One of the antimatter community current biggest eorts is to measure gravityon a neutral antimatter system, towards a rst test of Equivalence Principle- a cornerstone of General Relativity. Any deviation from the expected identicalbehaviour with respect to normal matter would be an indication of newphysics.This thesis explores the possibility to measure gravity with cold antihydrogen(H) produced with a novel pulsed scheme based on a charge-exchangereaction between antiprotons and Rydberg positronium (Ps). H and Ps arecurrently the only neutral antimatter systems available in quantities at lowtemperatures, and both are being considered for measuring gravity.Several results towards producing pulsed charge-exchange H were obtainedin the context of the AEgIS experiment. Positronium was produced with35% eciency in a dedicated setup, where spectroscopy of the 13S ! 33Ptransition and subsequent excitation to Rydberg levels were performed with 15% eciency (bandwidth limited). Ps was produced also in the cryogenicHproduction region of AEgIS (with 25% eciency), where 105 antiprotonswere also stored for minutes after capture, cooling, radial compressionand transfer. An estimate showed that 3?40 H atoms per measurement runcould be formed in the present setup.The experimental work motivated two detailed theoretical studies. A numericalcode for calculating Rydberg Ps energy levels and optical spectra inarbitrary (strong) external elds, based on a non-perturbative approach, wasdeveloped. Results well reproduced high-resolution spectroscopic data fromexperiments, and also demonstrated the feasibility of measuring both Ps axialand transverse velocity components using only transverse laser probes.A novel numerical method for calculating single-species non-neutral plasmaequilibria in cylindrical trap at low T was also developed, showing higher robustnessand faster convergence to solution (/ T?1) than currently availablemethods (/ T?2).Finally, the combined availability of the intense Ps source and the 13S ! 33Plaser made possible to observe the 23S metastable state of positronium byoptical decay from 33P, with a measured eciency of 1%. This resultrepresents a rst step towards a gravity measurement on metastable 23Spositronium.
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