Dipole-forbidden vibrational transitions in molecular ions : a novel route to precision spectroscopy and studying effects of interest to fundamental physics

Homonuclear diatomic molecules, such as H2 or N2, are usually not expected to show a vibrational spectrum. Although this is true within the electric-dipole approximation, higher-order terms in the interaction of matter and radiation give rise to very weak spectroscopic transitions. These “electric-dipole-forbidden” transitions are spectrally extremely narrow and thus of interest to precision spectroscopy and tests of fundamental physical theories by high-precision measurements. Until recently, such forbidden transitions have only been observed in neutral molecules, but not in molecular ions. In this thesis, we report the observation of electric-quadrupole rotation-vibration transitions in the molecular nitrogen cation N+2 — to our knowledge the first observation of a dipole-forbidden vibrational transition in a molecular ion. For this observation, N+2 ions produced state-selectively by photoionization of neutral N2 molecules were trapped in a radio-frequency ion trap (linear Paul trap) and cooled to millikelvin temperatures through interaction with cotrapped, laser-cooled atomic Ca+ ions (sympathetic cooling). Vibrational excitation of N+2 was achieved with high-intensity mid-infrared radiation from a frequency-stabilized quantum cascade laser. Vibrationally excited ions were detected through a state-dependent charge-transfer reaction of N+2 with Ar atoms. Addressing these extremely narrow transitions in a molecular ion enables the application of techniques developed for manipulation and control of atomic ions that exploit the long-range Coulomb interaction of charged particles, such as trapping, sympathetic cooling and non-destructive state detection through mapping of the quantum state to a cotrapped, experimentally more easily accessible ion (quantum logic spectroscopy). Besides reporting the observation of electric-quadrupole rotation-vibration transitions in a molecular ion, this thesis gives a detailed description of the mechanism underlying these transitions and a derivation of their line strengths in fine- and hyperfine-resolved spectra based on spherical tensor algebra. Moreover, a model for fine- and hyperfine-structure effects in molecular photoionization, an essential method for production of molecular ions, is presented. The model was successfully applied to analyze photoelectron spectra from the literature and is used to study future hyperfine-state-selective molecular photoionization schemes. Finally, a quantum-logic state-detection method for molecular ions is discussed. The method is based on state-dependent optical dipole forces acting on a hybrid molecular-atomic two-ion system. By inducing a geometric quantum phase, these forces map the state of the molecular ion onto the atomic one, from which it may be detected through interrogation of a closed optical cycling transition. Here, feasibility of this method for the N+2 -Ca+ system is positively assessed by estimating the relevant experimental parameters. Our observation and the theoretical framework developed here might considerably increase the precision and accuracy of molecular spectroscopy and therefore open up a new route to study fundamental scientific questions by means of high-precision molecular spectroscopy, such as a possible variation of fundamental physical constants or the search for yet unknown fundamental interactions