Departmental Oral Examination (Thesis Title: Photoassociation and Feshbach Resonance Studies in Ultra-Cold Gases of $^6$Li and Rb Atoms)
ABSTRACT:
This thesis presents an experimental apparatus capable of producing and studying ultra-cold mixtures of 
Li and Rb, and progress towards the creation of ultra-cold ground state Li
and LiRb molecules. In addition, we demonstrate the production of a BEC of Li Feshbach molecules, a degenerate Fermi gas of Li and the formation of BCS pairs. We discuss elements of the apparatus which are important to experiments with ultra-cold molecules. These elements include electric field plates in air capable of producing fields up to 18~kV/cm, and a laser system for photoassociation spectroscopy based on two Ti:Sapphire lasers phase locked to the same optical frequency comb. With respect to Li and 
Rb mixtures, we report on the observation of six Feshbach resonances, which represent an important step towards molecule production and future experiments in this heteronuclear mixture.
In the Li system, we report on the high resolution spectroscopy of the 
vibrational levels of the excited triplet potential and the 
vibrational levels of the excited singlet potential. In the excited singlet potential, we find that the 
and 
levels have the largest transition strength and are therefore good candidates to use as intermediate states in molecule formation. We demonstrate atom-molecule dark states in the BEC-BCS crossover regime and additionally use dark-state spectroscopy to make extremely high resolution measurements of the least bound 
ro-vibrational levels in the ground singlet and lowest lying triplet potential. In addition, we present spectroscopy of all ten and 
ro-vibrational levels in the lowest lying triplet potential and furnish a preliminary interpretation of the observed energy structure.
Finally, we report on the observation of anomalous Autler-Townes and dark-state spectrum. Using an extension to the standard three level model, we show that these anomalous profiles are due to degeneracies that exist in the bound molecular states, and to the choice of polarization of the coupling fields. These results have a direct impact on molecule formation, and provide a clear guide to future experiments.
