Rotation, vortex dynamics and disorder in non - equilibrium Bose gases

Abstract

Quantum fluids consisting of weakly-interacting atomic Bose Einstein Condensates (BECs) are superfluids, meaning they are able to flow without viscous effects. Superfluids have incredible properties, two of which are particularly interesting. Firstly, unlike the solid body rotation of a normal fluid, when a BEC is forced to rotate an array of quantized vortices is formed. These vortices are topologically protected defects which have a circulation with a fixed magnitude. Secondly, for a sufficiently slow velocity, the flow around an obstacle is a steady laminar flow and no vortices are nucleated; above some critical velocity, quantized vortices are nucleated signalling the appearance of dissipation in the system. In this thesis, we perform numerical and theoretical investigations in two dimensions into BECs which are forced to rotate, and into BECs which flow through a disordered potential. We present a method for evolving the projected Gross-Pitaevskii equation in an infinite rotating BEC, using quasi-periodic boundary conditions to investigate the behavior of the bulk superfluid in this system in the absence of boundaries and edge effects. We show that by choosing suitable simulation parameters, such as the size of the spatial grid and the number of energy levels considered, the numerical error of this method can be made negligible. Adding dissipation, we use our method to find the lattice ground state for a given number of vortices. We can then perturb the ground-state, to investigate the melting of the lattice at finite temperature. This method opens the door to be able to investigate the dynamics of the superfluid phase transition in a rotating Bose gas without edge effects. Although superfluid flow past a single obstacle is a well studied problem, far fewer studies have considered the case of a flow through a point-like disorder potential. We identify the relationship between the relative position of two point-like barriers and the critical velocity of such an obstacle. We then show that there is a good mapping between the critical velocity of a system with two barriers, and the critical velocity of a system with a large number of barriers. Driving a superflow through a disordered potential above the critical velocity, we use the projected Gross-Pitaevskii equation to study how the flow is arrested through the nucleation of vortices and the break down of superfluidity, a problem which has interesting connections to quantum turbulence and coarsening. We characterise the vortex decay as the effective width of the barriers is increased, and observe that vortex pinning becomes an important effect. Finally, we use a modified Point Vortex Model to model a number of quantized vortices which are subject to a continuously varying background potential. We investigate how the interplay of disorder strength and scale affect scaling laws in vortex dynamics.