Classical and quantum control of electrons using the carrier-envelope phase of strong laser fields

Electrons are among the lightest quantum particles in nature, yet they are of paramount importance in any kind of chemical reaction as they are the essence of molecular bonds. For several years, laser fields have been used towards the final goal of controlling chemical reaction dynamics. While early experiments focused mainly on the control of the internuclear wavefunction of rather heavy molecules, advances in shortpulse laser technology now allow the control of lighter molecules all the way down to hydrogen and even the direct control of electrons and their quantum wavefunctions. In this context, the stabilization and control of the carrier-envelope phase (CEP) of laser pulses has been one of the crucial technological advances that set off a revolution in ultrafast laser science. The authors review and summarize some of the past and current experimental achievements and theoretical ideas on CEP laser control of electrons. It will become clear that in some cases, depending on the control scenario, electrons can be considered to behave as classical particles and the control of their trajectories follow the laws of classical Newtonian mechanics while in other cases, the quantum nature of electrons is directly exploited to steer electron dynamics by means of quantum interference.