Dynamics of quantum vortices at finite temperature

TL;DR

This thesis investigates the finite-temperature dynamics of quantum vortices in Bose gases using classical-field theory, revealing how vortices nucleate, evolve, and interact with thermal components, and distinguishing vortex-liquid phases from thermal states.

Contribution

It introduces a classical-field formalism to analyze vortex dynamics at finite temperature, including vortex nucleation, relaxation, and the identification of vortex-liquid phases.

Findings

Finite-temperature condensates with vortices can be modeled as ergodic equilibrium states.

Vortex nucleation occurs via surface oscillations driven by thermal fluctuations.

Vortex-liquid phases are characterized by distinct temporal correlations from thermal states.

Abstract

In this thesis, we perform investigations into the behaviour of finite-temperature degenerate Bose gases using a classical-field formalism, focussing in particular on the dynamics of quantum vortices in these systems. We demonstrate that the coherence of the classical field can be characterised by its temporal correlations, and discuss how the phase-symmetry-broken averages familiar from mean-field theories emerge from the field trajectories. We show that a finite-temperature condensate containing a precessing vortex in a cylindrically symmetric trap can be realised as an ergodic equilibrium of the classical-field theory, and demonstrate the identification of the rotationally symmetry-broken condensate orbital and core-filling thermal component from the field correlations. We then consider the nonequilibrium dynamics that result when such a precessing-vortex configuration is subjected to a static trap anisotropy which arrests its rotation, and observe novel coupled relaxation dynamics of the condensed and noncondensed components of the field. Finally, we consider the nucleation of vortices in an initially zero-temperature quasi-two-dimensional condensate stirred by a rotating trap anisotropy. We quantify the emergence of a rotating thermal component of the field, which drives the nucleation of vortices from condensate-surface oscillations, and study the relaxation and rotational equilibration of the initially turbulent collection of vortices. We find that thermal fluctuations of the field prevent the vortices from settling into a rigid crystalline lattice in this reduced dimensionality, and that true condensation in the field is completely destroyed by the disordered motion of vortices. We show, however, that the temporal correlations of the field distinguish the quasi-coherent vortex-liquid phase in the trap centre from the truly thermal material in its periphery.