Superfluidity and Supersolidity in Ultracold Atomic Gases Beyond Mean Field

Sammanfattning: This thesis investigates ultracold bosonic systems using an extended mean-field formalism with a focus on their superfluid and supersolid properties. The dissertation comprises five chapters and four articles, where the chapters provide some background to the research put forward in articles.Paper I demonstrates the existence of multiple singly-quantized vortices in two-dimensional droplets made out of binary Bose mixtures, and discusses the possibility of using metastable persistent currents to generate self-bound vortex-carrying states.Paper II studies metastable persistent flow in dipolar supersolids in ring-shaped trapping potentials and gives a criterion for when such flow can exist. Hysteretic effects are investigated and found to depend qualitatively on the fraction of non-classical rotational inertia of the system.Paper III presents results regarding the validity of using a super-Gaussian ansatz when describing two-dimensional self-bound droplets in Bose-Bose mixtures, and it is found that most quantities are well-described by employing such an ansatz. Furthermore, the breathing mode of droplets with and without vorticity is studied.Paper IV investigates droplet-superfluid compounds in one-dimensional binary Bose mixtures trapped by means of periodic boundary conditions. It is found that such configurations have a fraction of non-classical rotational inertia larger than zero but smaller than unity at zero temperature. It is demonstrated that this fraction is not equal to the residual superfluid part of the system due to the superfluid's response to the motion of the localized parts.