Ramsey-comb spectroscopy on molecular deuterium and hydrogen-like helium: experimental and numerical studies

There exist several physical phenomena that cannot currently be accounted for by physics theories. Therefore, spectroscopists search for ever finer details in atomic and molecular spectra hoping to find clues to these phenomena. The work described in this thesis contributes to this research effort. We present experimental results on spectroscopy of the deep ultraviolet 202 nm X - EF transition in molecular deuterium, measured with an uncertainty of 19 kHz with the Ramsey-comb spectroscopy technique. We also present experimental results for the first laser excitation of the 1S-2S transition in He+ at 32 nm and present an in-depth feasibility study of Ramsey-comb spectroscopy of the 1S-2S transition on trapped and laser-cooled He+, featuring extensive numerical results mapping out the parameter space in which a precision measurement is expected to be possible. Additionally, we present a Graphics Processing Unit-accelerated routine to simulate the propagation of intense ultrashort pulses through an atomic gas which achieves significant (up to almost 200) speed-up factors relative to a naive Central Processing Unit implementation of the same routine.