Molecular Structure and Production of Ultracold \({ }^{88}\mathrm {Sr}_2\) in an Optical Lattice

This chapter serves a pedagogical purpose. I describe the molecular structure of the most abundant isotopologue of diatomic strontium and the molecular potentials pertinent to this thesis. I discuss selection rules for molecular transitions mediated by a laser field, molecule formation, and state-selective detection through photochemical processes; i.e., photoassociation and photodissociation. Finally, I summarize the mathematical treatment of a particle confined in a one-dimensional periodic potential, which serves as a segue to discussions of the Lamb-Dicke and resolved-sideband trapping regimes, recoil-free molecular spectroscopy, and spectroscopy-based thermometry techniques for ultracold molecules.