Quantum degenerate molecular gases are of interest for the unique level of control they offer over chemical interactions and processes. To reach the quantum degenerate regime, these molecular gases must be cooled to ultracold temperatures, typically on the order of 100 nanoKelvins. Unlike atoms, with a few-level system that facilitates cooling, molecules represent a many-level system, which makes these temperatures experimentally difficult to achieve. As a result, experiments have turned to photoassociation and Feshbach resonance as shortcuts to form ultracold molecules from already ultracold atoms. Photoassociation and Feshbach resonance have been utilized to successfully create stable quantum degenerate molecules, but not on a routine basis, and only for a small range of molecular species. The primary focus of this thesis will be to study photoassociation and Feshbach resonance, and investigate possible routes to more efficient long-lived quantum degenerate molecule formation. We will also investigate realistic limiting conditions to open the possibility to more routine molecules, and to molecular species that are currently inaccessible. Overall, we find combined photoassociation and Feshbach resonance are viable schemes for efficiently creating quantum degenerate molecules, under realistic restrictions such as low laser intensity, narrow Feshbach resonance, and strong elastic collisions. As the techniques to create quantum degenerate molecules become more robust and experimentally available, the creation of colder, larger, and more long-lived samples will facilitate study of these molecules, and spur development into new applications. / Physics

<p dir="ltr">Abstract: The field of singly-trapped ultracold molecules has expanded rapidly in the past few years. With the introduction of fast tweezer rearrangement and the demonstrated viability of ground-state preparation by magneto-association coupled with STIRAP, powerful and robust arrays of ultracold molecules for quantum information science are finally being realized after decades of research. This dissertation primarily discusses the engineering associated with the conventional path toward creating arrays of LiCs molecules trapped in optical tweezers. Scientific results of the successful trapping and sub-doppler cooling of both atoms to release-recapture temperatures of less than 100uK are discussed. Discussed is also recent unpublished work focusing on atomic state preparation in optical tweezers, merging of the two species, and observation of Feshbach resonances of the pairs of atoms.</p>