Similarities and differences between highharmonic generation in atoms and solids [Invited]

The basic features of high-harmonic generation in dilute atomic gases and solid-state systems are analyzed using a microscopic many-body theory. Whereas it is sufficient for atomic gases to include the ground state and the ionization continuum, the semiconductor approach has to deal with the relevant interband polarizations and intraband currents. For both systems, a closed set of Bloch-type equations is derived, which has to be solved numerically. As common features, the emission of odd-order harmonics, the development of a plateau, and a high-frequency cutoff are observed if the solid system is modeled as a two-band system. However, already the addition of a third coupled band effectively breaks the inversion symmetry and leads to the appearance of even harmonic orders with comparable strength. In all cases, frequency-and time-resolved studies reveal a fundamentally different timing in the emission dynamics of the individual frequency components in atomic and solid-state systems, which can be attributed to the presence of energy bands in solids.