Modern pulsed laser systems are able to produce strong electric fields similar to that within atoms and with durations comparable to the evolution of their electronic wave functions on the sub-femtosecond time scale. Accordingly, processes driven by such pulses are of considerable interest for many reasons. In particular, they provide precise tests of the role of time within quantum mechanics. Theoretical understanding of these problems is complicated in this non-perturbative regime, necessitating the use of high power computational methods.

This presentation will provide an overview of the work we have conducted on several of these laser driven processes by means of the brute force numerical solution of the time-dependent Schrödinger equation. Specifically we will discuss: the attoclock, a setup designed to clock the escape of an electron as it tunnel ionises; reconstruction of attosecond beating by interference of two-photon transitions (RABBITT), a pump-probe spectroscopic technique to extract phase information in photoionisation; high harmonic generation, the process by which femtosecond pulses are converted into attosecond; and the acceleration of neutral atomic species by large electric field gradients, a novel problem that goes beyond the commonly employed treatment of the laser field as spatially uniform with respect to the atom.