This dissertation details of the construction of and experiments performed in a hybrid system consisting of a cold neutral atomic magneto-optical trap (MOT) contained within a linear radio-frequency quadrupole ion trap (LQT). The combination of these two workhorses of atomic physics facilitates a variety of developing science such as the controlled investigation of ion-neutral quantum chemistry and the production of ground-state molecular ions. While the primary focus of this work is the production of ultracold molecular ions via sympathetic cooling, there has been investigation of cold (T ~ mK) ion-neutral charge exchange processes in two different ion-neutral pair systems. In addition, a possible method of producing ultracold homonuclear molecular ions via a photo-associative ionization (PAI) pathway is studied in the MOT. The LQT traps ions in spatial overlap with a ⁴⁰Ca MOT constituting an ultracold buffer gas purposed to sympathetically cool molecular ions.

An effective, general method of producing ground-state molecular ions would open a field of physics allowing, for example, precise measurements of molecular transitions which are uniquely sensitive to parity violation, or the possible variation of fundamental constants. Another promising application of cold molecular ions is an implementation of a quantum computing architecture by coupling micro-fabricated strip-line resonators to the microwave rotational transition found in many diatomic molecular ions. The molecular ion BaCl⁺ is chosen to be used in proof-of-principle sympathetic cooling experiments. Ultimately, a vibrational internal state thermometry experiment shows that the Ca MOT performs very efficiently at quenching the vibrational motion of the BaCl⁺ molecular ion.

As a product of overcoming experimental challenges, this thesis discusses several experiments to characterize trapping and reaction dynamics in the hybrid system. For example, charge transfer measurements are performed with two different laser-cooled atomic ion species, Yb⁺ and Ba⁺, which are allowed and disallowed ground-state reaction, respectively. Controlled measurements of these inelastic processes test the cutting edge of quantum theory of ion-neutral interaction in both the ground-state and under optical excitation.