Frontiers of atomic high-harmonic generation

In the past two decades high-harmonic generation (HHG) has become a key process in ultra-fast science due to the extremely short time-structure of the underlying electron dynamics being imprinted in the emitted harmonic light bursts. After discussing the fundamental physical picture of HHG including continuum--continuum transitions, we describe the experimental progress rendering HHG to the unique source of attosecond pulses. The development of bright photon sources with zeptosecond pulse duration and keV photon energy is underway. In this article we describe several approaches pointed toward this aim and beyond. As the main barriers for multi-keV HHG, phase-matching and relativistic drift are discussed. Routes to overcome these problems are pointed out as well as schemes to control the HHG process via alterations of the driving fields. Finally, we report on how the investigation of fundamental physical processes benefits from the continuous development of HHG sources.