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Abstract

The work of this thesis demonstrates single-ion nondestructive spectroscopy of molecules in Penning traps. Due to their rovibrational level structure and the close proximity of at least two nuclei, molecular ions exhibit unique sensitivities for tests of the Standard Model of particle physics. In particular, a high-precision comparison of rovibrational transition energies of H2+ and its antimatter counterpart anti-H2+ promises to stringently test for violations of the fundamental charge-parity-time reversal symmetry [1, 2]. Here, a new method for nondestructive readout of the internal quantum state of a single molecular hydrogen ion (MHI) was demonstrated, along with external production and several month-long confinement in a Penning trap, which are among the requirements for future measurements of anti-H2+. The internal quantum state - vibrational, rotational, hyperfine, Zeeman - of the MHI was determined via millimeter wave-induced resonant electron spin flips (eSF) employing the continuous Stern-Gerlach effect [3]. This was applied for spectroscopy of all six eSF transitions in the rovibrational ground state of HD+, resulting in the determination of the bound-electron ge(0, 0) factor to 0.20 ppb and the spin-spin interaction coefficients of the hyperfine structure (HFS), E4(0, 0) and E5(0, 0), to 44 ppb and 151 ppb, respectively. The experimental precision of ge(0, 0) exceeds the precision of the current theoretical prediction by almost three orders of magnitude [4]. Our value also shows agreement with a new, still unpublished calculation, which surpasses the experimental precision. Precise values of ge factors allow the unambiguous internal quantum state detection of MHI. E4(0, 0) and E5(0, 0) probe HFS theory below the ppm level, which enters the prediction of rovibrational transition frequencies. The near-agreement of the values does not explain deviations observed in rovibrational measurements [5]. Furthermore, efforts towards applying the developed methods to high-precision rovibrational spectroscopy in Penning traps are presented.