Solitons, vortices and shell structure in ultracold atomic quantum systems

Sammanfattning: This dissertation deals with finite-size effects in a few different quantum many-body phenomena in ultracold atomic systems. The finite-sized systems were simulated numerically using both mean-field methods and methods beyond mean-field, e.g. quadratic configuration interaction and exact diagonalization. The thesis is based on five scientific papers:Paper I is about the finite-size effects in the dynamics of a few-body soliton-like state. The collapses and revivals of the solitary wavefront in the particle density is characterized both analytically and numerically in the limit of weak interactions.Paper II analyzes a scheme to renormalize the contact interaction when used for exact diagonalization in a two-dimensional space. By relating the coupling strength in the diagonalization using the two-particle system, for which regularized solutions exists, converged results are obtained.Paper III deals with the formation of quantized vortices when stirring a harmonically trapped finite-sized system with a quadrupole deformation. I the energy spectrum the avoided crossing is found to be described by either of two types of correlated states. The type of avoided crossing can be controlled by the inclusion of an extra quartic deformation. Hysteresis in the mean-field description is found to be related to the types of avoided crossings exhibited and the full many-body time-evolution is compared to mean-field results. Paper IV investigates vortices in rotating fermionic droplets with dipole-dipole interactions. The vortex structure is found to still be present after the interaction is made anisotropic by having the dipoles tilt. Paper V contains an investigation of the effects on shell structure in fermionic droplets with dipole-dipole interactions. For a anisotropic harmonic oscillator, by tilting the dipoles, the shell structure of an isotropic oscillator can be restored.