The Hallmarks of Superfluidity in Exotic Phases of Bose Gases : Self-bound Droplets, Mixed Bubbles and Supersolids

This thesis investigates superfluidity in exotic phases of ultracold bosonic gases, namely self-bound droplets, mixed bubbles, and dipolar supersolids. We investigated these systems analytically and numerically using an extended Gross-Pitaevskii and Bogoliubov-de Gennes formalism. The dissertation offers six chapters, providing the necessary derivations to build the required background and understanding for the six papers this thesis comprises of:In Paper I, we show that two-dimensional self-bound droplets in a bosonic mixture can support multiply singly-quantized vortices and give a protocol to create self-bound meta-stable persistent currents carrying vorticity.Paper II studies the ground state properties of two-dimensional droplets via a super-Gaussian variational ansatz, showing excellent agreement with numerical solutions. Furthermore, we study whether the breathing mode is a feasible excitation in these droplets with and without vorticity.In Paper III, we numerically demonstrate the existence of mixed bubbles near phase separation in a one-dimensional torus. These mixed bubbles coincide with a Higgs-Amplitude mode in the excitation spectrum. Additionally, we show that metastable persistent currents can occur, and the associated avoided level-crossing opens intriguing prospects for atomtronic concepts.Paper IV investigates a dynamic stirring process in a toroidal dipolar supersolid with a weak link. The weak link couples two angular modes, allowing phase slips to occur under rotation. These phase slips induce a dynamic self-organizational process of continuous melting and re-freezing of crystal sites in the supersolid.In Paper V, we demonstrate the existence of one-dimensional self-bound droplets in the few-body regime using exact diagonalization and compare these results to mean-field solutions. Across the transition from superfluid to self-bound droplet, we find the few-body precursor of a Higgs-Amplitude mode and observe a change in the rotational dispersion relation from negative curvature to parabolic.Lastly, Paper VI investigates the decoupling of first sound, second sound, and Higgs-Amplitude mode across the superfluid-supersolid transition in a toroidal dipolar supersolid. These modes emerge from their elementary excitations, and we propose experimental protocols to probe these sound and amplitude modes selectively.