Attosecond spectral singularities in solid-state high-harmonic generation

High-harmonic waves are generated from a MgO crystal under experimental conditions where the simple semi-classical analysis fails. High-harmonic generation spectroscopy directly probes the strong-field attosecond dynamics over multiple bands. Strong-field-driven electric currents in condensed-matter systems are opening new frontiers in petahertz electronics. In this regime, new challenges are arising as the roles of band structure and coherent electron-hole dynamics have yet to be resolved. Here, by using high-harmonic generation spectroscopy, we reveal the underlying attosecond dynamics that dictates the temporal evolution of carriers in multi-band solid-state systems. We demonstrate that when the electron-hole relative velocity approaches zero, enhanced constructive interference leads to the appearance of spectral caustics in the high-harmonic generation spectrum. We introduce the role of the dynamical joint density of states and identify its mapping into the spectrum, which exhibits singularities at the spectral caustics. By studying these singularities, we probe the structure of multiple unpopulated high conduction bands.