Quantum Theory of Complex Ultracold Collisions

Abstract

This thesis reports on a variety of calculations on cold and ultracold scattering, with a broad theme of how best to consider and understand complex systems in simple ways.

Firstly, we investigate quantum defect theory. We demonstrate that it is not only an excellent model for simple systems, but can also provide simple predictions of the of possible behaviours for complex systems, in particular for a model of collisional losses. These predictions agree well with expensive coupled-channels calculations in cases where the full calculations also predict only the range of possible behaviours.

Secondly, we consider effects relating to thermalisation of cold and ultracold gases. We show that considering the correct transport cross section, , is important for determination of scattering lengths and their signs by interspecies thermalisation. This cross section is also important to the understanding of high-quality simulations of sympathetic cooling in a microwave trap, which suggest Rb is likely to be a good coolant for CaF. We also correct an error in the interpretation of previous results for sympathetic cooling in a magnetic trap, showing this may work from over 100 mK for Li+CaF and many Kelvin when using atomic hydrogen as a coolant.

Thirdly, we study quantum chaos in ultracold collisions. We find very clear and strong signs of chaos in Li+CaH. We also show that a more strongly coupled system, Li+CaF, is fully chaotic and that there is unexpected structure in the levels of chaos as the CaF rotational constant is varied. We also show that signatures of chaos can emerge in a very simple atom-atom system, Yb()+Yb(), which interacts on only two Born-Oppenheimer potentials.

Finally, we examine the idea that metastable states in 2-body scattering greatly enhance 3-body recombination at ultracold temperatures. We attempt to put it on a more rigorous theoretical grounding by considering Smith's collision lifetime and related quantities, but those are shown to lack clear interpretations in the ultracold regime. We therefore consider 3-body scattering theory and arrive at some general conclusions about how we expect such 2-body features to appear in 3-body scattering and suggest possible ways forward.