Strong-Field Interference of Quantum Trajectories with Coulomb Distortion and Electron Correlation

This thesis explores quantum interference patterns present in the strong-field phenomena of above-threshold ionisation and non-sequential double ionisation, which correspond to one and two ionisation processes, respectively. For above-threshold ionisation a new model is explored that uses Coulomb-distorted quantum trajectories to produce the transition amplitude of the process. This method is one of only a few semi-analytic models to account for the Coulomb potential for electrons in the continuum. The quantum trajectories utilised in this model lead to a myriad of interference patterns, some of which have never been identified before and the signature of most can be found in experimental results or \textit{ab-initio} solutions of the time dependent Schrödinger equation. Given the recent interest in using such interferences for holographic imaging of atoms and molecules, conditions and an analytic model are formulated to better understand the potential of this new imaging process. The role of recollision is also investigated and how trajectories in this new model relate to well known direct and rescattered trajectories from above-threshold ionisation models employing the strong field approximation. Subsequently, interference is examined for the case of non-sequential double ionisation for the recollision with subsequent ionisation mechanism using the strong field approximation. Many types of interference patterns are found, where previously it was expected that interference would not play a role. These patterns are investigated in detail and conditions formulated for them. The model is extended to different lengths of laser pulses by incorporating a particular superposition of intermediate excited states in the process in order to replicated experimental data, opening up the possibility of using experimental data to reconstruct the intermediate excited state of the second electron in the non-sequential double ionisation process