Positronium laser excitation in the AE$\bar{g}$IS experiment

The AEgIS experimental program on antimatter systems involves the formation of antihydrogen atoms for gravitational and CPT studies. One of the key ingredients of the AEgIS strategy for the synthesis of antihydrogen atoms is the creation and manipulation of Positronium (Ps) atoms laser excited to Rydberg states (n > 15). In AEgIS, Ps is produced in bunched mode and the Rydberg excitation is achieved with a two laser pulse technique, by passing through a n = 3 intermediate level. Because excitation on Ps n = 3 state has never been proposed before, in AEgIS a dedicated experimental apparatus and several detection strategies have been studied in order to observe the first measurement ever on this interesting process. In this work we present and discuss the experimental findings about the successful Ps n = 3 excitation. Moreover, in this thesis, a study of the impact of involved nonlinear processes on the excitation efficiency of a Doppler broadened atomic cloud is carried out. Presented simulation results show that, by exploiting properly nonlinear processes in the generation of the desired wavelength, it is possible to improve the excitation efficiency of a laser pulse. It is crucial, in AEgIS, the use of a periodically poled crystal in quasi phase matching regime. This gives a broadband continuous output spectrum whose wings survive to the spectral cutting of the last nonlinear crystal of the chain (which has insufficient spectral acceptance). This means that, at high laser energies, these wings can be amplified and the spectrum gaps can be filled in, leading to high reachable saturation efficiencies. On the contrary, in a laser pulse with a comb-shaped spectrum with a Gaussian envelope, both wings and gaps drop rapidly to zero, and amplification hardly occurs at usually employed energy regimes. The presented model is finally used to fit AEgIS Ps n = 3 excitation experimental data.