Phase space analysis of quantum effects in strong field ionisation

This thesis explores quantum effects during strong field ionisation, with emphasis on both classical and quantum phase-space interpretational tools. Specifically, this involves investigating the presence of momentum gates during the enhanced ionisation of H₂⁺. These structures cycle through the momentum space without following the time-profile of the external field. By computing autocorrelation functions and Wigner quasiprobability distributions, we establish that momentum gates may occur for static driving fields, and even for no external field at all. Their primary cause is an interference-induced bridging mechanism that occurs if both wells in the molecule are populated. Their cyclic motion in momentum space has a non-classical evolution, as seen from the quantum Liouville equation. Additionally, we employ the quantum trajectory method to seek another criteria for non-classicality. Using an analytical method, we then compute the different eigenfrequencies governing the system in a field-free setting. This provides an in depth understanding that is applied to the time-dependent case. There, the frequency of the quantum bridge, intrinsic to the molecule, is higher than that of the external field. This leads the quasiprobability distribution to sometimes counter-intuitively flow in the direction opposed to the electric-field gradient. These ionisation mechanisms form an optimisation problem that can be controlled using the appropriate molecular targets, driving fields and coherent superposition of states. We investigate the impact of multiple parameters at once by employing machine learning dimensionality reduction techniques. This allows us to disentangle the different effects at play and establish a hierarchy of parameters for controlling ionisation. The features encountered are explained with phase-space arguments and optimal conditions are found for both static and time-dependent fields. The conclusions presented throughout this thesis can in the future be expanded towards multielectron systems, incorporating decoherence and multiple degrees of freedom