Abstract
The ultracold regime provides a unique opportunity to study quantum phenomena, and ultracold atomic systems have hosted a variety of hallmark quantum many-body experiments, from the BEC-BCS crossover to quantum droplets. These experiments are only possible as one can exert exquisite control over the atomic interaction using collision resonances, which are ubiquitous in atomic and particle physics.
This thesis considers the scattering behaviour in the vicinity of two interacting collision resonances, observed experimentally in rubidium-87 and discussed in two distinct theoretical frameworks. Firstly, quantum defect theory separates out the different length and energy scales involved in atomic collisions which highlights the effects of scattering near threshold and provides an excellent agreement with the experimental observations. Secondly, the resonance interaction is cast into the concept of the analytically-continued S matrix, which hosts poles at complex energies corresponding to each resonance. These poles undergo an avoided crossing in the system studied here.
Machines for producing ultracold atoms, such as that found at Otago, are generally complex research instruments. The Otago machine additionally provides a case study for online health monitoring and automated optimisation of the machine parameters. This thesis presents a health monitoring framework which is suitable for retro-fitting to existing
experiments, improves the robustness of the Otago apparatus and decreases fault-diagnosis times.