High-order harmonic generation (HHG) is a fundamental nonlinear optical phenomenon that originates from the strong light-matter coupling. HHG was first observed and studied in gas systems, and recently HHG in condensed matters, in particular semiconductors, has attracted much attention. In semiconductors, HHG is well explained by the independent motion of individual electrons, which makes the spectroscopic application of HHG for band information possible. In this talk, we explore the potential of HHG in condensed matter even further. Namely, we study HHG in strongly correlated systems. We discuss the origin and characteristics of HHG in Mott insulators, and reveal its connection with many-body excitations, which can make the HHG spectroscopy of many body information possible.

Firstly, we reveal that the HHG in Mott insulators can be understood as the recombination process of photo-excited local multiplets such as doublons and holons [1,2]. In particular, in the one dimensional systems, where the exact dispersion of the many body elemental excitations is available, we show that the semiclassical three step model combined with the many body information is applicable to explain the HHG process in the Mott insulator. The result suggests that HHG can be a direct measure of the many body excitations. Secondly, we discuss the effects of the correlations between different degrees of freedoms, such as spin and charge, on HHG in strongly correlated systems [3]. We show that the strong correlation leads to anomalous behavior of HHG, where the HHG intensity is exponentially enhanced with the increase of the gap size. Our analysis consistently explain the recent report of the similar anomalous behavior of HHG in Ca2RuO4. The result indicates that the entanglement of multiple degrees of freedom, which is characteristic of strongly correlated systems, has nontrivial and important effects on the nonlinear optical response.