Confined Bose superfluids: a study of vorticity in a rotating bucket, and phase transitions and sound in a trap from two to three dimensions

Abstract

Quantum fluids are a fascinating state of matter, permitting extraordinary insights into the behaviour of macroscopic quantum systems. Most strikingly, they possess the property of superfluidity, enabling inviscid flow. Whilst irrotational in nature, singularities in the fluid provide localised vorticity in the form of quantised vortex filaments. Interaction between these vortex structures provides rich dynamical behaviour which is interrogated within the first part of this thesis. Furthermore, one expects the equilibrium and dynamical proper ties of a trapped superfluid system to vary in response to changes in dimensionality. Whilst dimensionality crossovers have previously been considered both experimentally and theoretically, the nature of the dimensional crossover between the 2D and 3D phase tran sitions in a trapped Bose gas remains relatively unexplored and forms the secondary focus of this thesis. Initially, we consider the effects of disordered potentials, protuberances and remnant vor tices for a zero temperature weakly interacting Bose gas under rotation. Focusing partic ularly on a rough bucket potential we draw parallels with superfluid helium experiments, where such effects must be considered. Our findings elucidate important insights on the effects of vortex proliferation in the spin-up dynamics of a quiescent system towards the simple and well-reproduced vortex lattice structure. We then go on to discuss the effects of dimensionality on the finite temperature weakly interacting Bose gas, this time concentrating on a hybridised optical trap that allows one to modify the trapping strength along a singular direction. Utilising the stochastic pro jected Gross-Pitaevskii equation (SPGPE) we validate our approach based on previous findings at the dimensional extremes before considering in greater detail, the precise na ture of the crossover region. We introduce a novel mixed basis numerical scheme to solve the SPGPE in the hybridised geometry. Using this, we identify and numerically extract a phase transition temperature as a function of dimensionality using a collection of equilib rium statistics. Building on this work, we subsequently conduct a numerical investigation into the propagation of sound as a function of dimensionality in the trapped Bose gas. We discover new insights on the properties of the sound across the phase transition at the dimensional extremes. We then extend our work into the dimensionality crossover region, paying particular attention to the behaviour of the sound at the phase transition critical point.