CHAPTER 2: Low-dimensional Models for Simulating Attosecond Processes in Atoms and Molecules

We present the implementation and utilisation of simple yet efficient low-dimensional models to simulate the response of atomic and molecular systems to light pulses, from the perturbative to the strong field regimes, with direct applications to attosecond sciences. The motivation is that solving the time-dependent Schrödinger equation for such simple models often proves more useful to get a clear physical picture than solving it for a full-fledged multi-dimensional model. We have focused the chapter on one- and two-dimensional approaches with illustrations on high-order harmonic generation and the photoionisation processes that are essential in an attophysics context. Within this framework, the topics we shall consider are the modelling of various aspects of high order harmonic generation in atoms and molecules (emission times, quantum path interferences, influences of the internuclear structure and dynamics) and the investigation of near threshold photoemission of a diatomic molecule with vibronic resolution from a time-dependent perspective. The advantages and limitations of low-dimensional models are discussed through the chapter.