Few-Body Quantum Rings : An Exact Diagonalization Approach

This thesis investigates few-body quantum rings, particularly in the study of ultracold bosonic gases and nanowire quantum dots. These systems are investigated numerically using exact diagonalization methods. This dissertation contains five chapters which develop numerical and theoretical background for understanding the few-body calculations and analysis contained in the four included papers: Paper I explores the formation of few-body analogues to self-bound quantum droplets in binary bosonic mixtures in one dimension. Signatures of spontaneous symmetry breaking associated with localization in the ground state are observed in the low-lying energy spectra. This interpretation of the spectra is supported by the ground state pair correlations and an analysis of the dynamical properties of the system via the transition matrix elements. Paper II provides a mini-review of some important concepts in the field of highly-dilute self-bound quantum droplets, including a discussion of the signatures of droplets in the few-body limit. Paper III demonstrates that a quantum dot formed in the cross section of an InAs nanowire can be tuned to generate an energy spectrum consistent with that of an ideal quantum ring. It is shown that the strong spin-orbit interaction experienced by electrons confined to this rotationally symmetric potential is protective against orbital scattering in the presence of a perturbation to the potentials rotational symmetry. Paper IV investigates localization in few-body bosonic systems with a single impurity. The presence of few-body precursors of Higgs-Anderson and Nambu-Goldstone like modes are observed in the theoretical energy spectra. By tuning the impurity-boson mass ratio, the transition from a spontaneous to an explicit breaking of the rotational symmetry of the ring system is investigated.