Abstract

The technological development of ultrashort laser pulses makes it possible to monitor and control the dynamics of the electrons in atoms and molecules. In this Chapter we first review recent experimental and theoretical progress towards tracking and understanding of electron motion in nature’s simplest molecule, the hydrogen molecular ion, on its natural time scale. A complex and counterintuitive dynamics appears due to a strong coupling between different electronic states and of the electron with the external field. Different approaches for the observation of these single-active electron effects in the hydrogen molecular ion as well as of electron rearrangement in the valence shell of more complex molecules are presented. Based on these new insights we then turn to a discussion of recently proposed strategies to control electron localization in molecules with carrier-envelope phase locked pulses, attosecond pump-probe set-ups as well as circularly polarized laser pulses. In particular, results of experiments, in which the asymmetry of localization probabilities at the protons in the hydrogen molecular ion is observed, are complemented with theoretical results and analysis from ab-initio numerical simulations.

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