Ultrafast physics, which encompasses phenomena occurring at the attosecond scale, provides the foundation for understanding electron dynamics in atoms, molecules, and materials. To explore this realm, ultrashort laser pulses are utilized as powerful tools for discerning dynamics and unraveling the underlying physics. By varying the laser polarization and employing pulse combinations, a wide range of intriguing ultrafast phenomena can be probed. In this thesis numerical simulations, specifically of the interaction of atoms with circularly and elliptically polarized pulses, are used to shed light on the fascinating dynamics exhibited by atoms when subjected to intense ultrafast laser irradiation.
We first provide an overview of the dynamics that form the basis of the research conducted and the numerical methods employed to model the atom-laser interaction through the solution of the time-dependent Schrodinger equation. Building upon this foundation we then delve into the investigation of atoms interacting with bichromatic circularly polarized laser pulses. The distribution of population among various excited states is examined, and a new mechanism is proposed to explain the results. Next, we shift our focus to the analysis of photoelectron spectra generated by the ionization of atoms interacting with circularly and elliptically polarized pulses. The study specifically considers the effects of different initial magnetic states on the resulting spectra, shedding light on the underlying electron emission process. Lastly, we present two new numerical methods: A Monte Carlo simulation technique is introduced as a means to study electron dynamics and ionization in laser fields of long wavelengths. Second, an ab-initio solution for diatomic systems, based on the single-active-electron and Born-Oppenheimer approximations, is developed, applied, and tested.</p