Non-equilibrium and finite temperature trapped Bose gases :interactions and decay of macroscopic excitations

Abstract

In this thesis we study the dynamics of dark solitons, vortices and Josephson effects, in trapped atomic Bose-Einstein condensates. We firstly demonstrate a novel, sound mediated, long-range interaction mechanism between dark solitons using the Gross-Pitaevskii equation. Then we present the effect of finite temperatures on the dynamics of vortices and Josephson effects using a generalised form of this equation, which additionally includes a source term modelling the coupling of the condensate to a fully dynamical thermal cloud, described by a quantum Boltzmann equation. The latter formalism is known as the Zaremba-Nikuni-Griffin scheme (ZNG). The sound-mediated interaction between dark solitons is such that the speed and trajectory of one soliton in a condensate confined by a harmonic trap can be significantly modified by the presence of a second soliton in the same trap. By confining the two solitons to spatially separated subregions of a double well trap, we show how this effect can be magnified. In particular we find it can be large, and therefore detectable, in experimentally relevant geometries, including high-periodicity optical lattices in which the ability of solitons to act as both absorbers and emitters of energy becomes apparent. At finite temperatures, we model the dynamics via the ZNG scheme. Firstly, we give a detailed description of the scheme for numerically solving these coupled equations including all collisional terms. Then we study the effect of a dynamical thermal cloud on vortex dynamics, in particular, focussing on the experimentally-relevant quantities of precession frequencies, decay rates and vortex core brightness. The changes in these are found to increase with increasing temperature for a pancake-shaped geometry, in particular for trapping parameters of a recent experiment of Freilich et al. (Science 329, 1182 (2010)). Particle exchanging collisions between the condensate and thermal cloud are found to be crucial in determining the rate of decay of a precessing vortex. We further show that, rotation of the thermal cloud can be a mechanism for radially translating the position of a vortex, a scenario under current investigation. Finally, we analyse the effect of finite temperatures on population dynamics in a double well atom chip experiment by LeBlanc et al. (Phys. Rev. Lett. 106, 025302 (2011)). Focussing on the coupled evolution in the absence of collisions, we find that it generates significant damping which is, however, less than that observed in the experiment. A detailed comparison in the presence of collisions is beyond the scope of this thesis.