Ultracold Molecules for Quantum Science: Theories of Molecule Formation

The formation of ultracold molecules is the overarching focus of this thesis. We undertake a number of calculations to explore a variety of systems and the different techniques that can be used to produce them at ultracold temperatures. Magnetoassociation is routinely used to associate pairs of alkali-metal atoms to- gether to produce alkali-metal dimers. Magnetoassociation exploits the zero-energy magnetically tuneable Feshbach resonances that exist in ultracold atomic and molec- ular collisions. We study the near-threshold bound states that cause Feshbach res- onances in ultracold 39K + 133Cs collisions. In order to generate an accurate model of the interatomic 39K133Cs potential we undertake an interactive non-linear least- squares fit to a number of experimental measurements. Using Feshbach resonances to control the interactions between atoms and molecules at ultracold temperatures is an important avenue of research. Coupled-channel cal- culations are used to investigate resonances in Rb+CaF collisions. The quantity, and characteristics, of these resonances are determined by the atom-molecule in- teraction potential, which is yet to be modeled accurately. We utilize a number of representative potentials to explore what the spectrum of Feshbach resonances may look like. Mergoassociation is a new way of making molecules at ultracold temperatures. We develop a theory for pairs of nonidentical nonspherical traps and a coupled- channel approach for the relative motion of the two atoms. We study mergoassoci- ation for pairs of cylindrically symmetrical traps as a function of their anisotropy. We also develop a basis-set method for the relative and center-of-mass motions of the two atoms. We consider the example of RbCs and then extend the treatment to other systems where mergoassociation may be effective, namely RbSr, RbYb and CsYb.