High-harmonic generation in strongly correlated systems

The recent development of strong lasers enables us to study various nonlinear optical phenomena. One fundamental example is high-harmonic generation (HHG). HHG was observed and intensively studied first in gases, and later in semiconductors. More recently, the scope is further extended to strongly correlated electron systems (SCESs). SCESs are a potentially interesting playground for the HHG research since i) the excitation structures cannot be described by independent electrons and holes unlike conventional semiconductors, ii) various degrees of freedom (charge, spin and orbitals) can be strongly intertwined in SCESs and iii) SCESs host intriguing phases. Due to these properties, HHG in SCESs may show peculiar properties absent in HHG in semiconductors.



Here, we discuss the basic feature and origin of HHG in Mott insulators described by the single-band Hubbard model, a standard model for SCESs [1-3]. In the Mott phase, each site is occupied by a single electron, and it cannot move due to the strong on-site Coulomb interaction. Photo-excitation creates doubly occupied sites (doublons) and no occupied sites (holons). They are charge carriers of this system and their dynamics leads to the light emission. Firstly, we reveal a generic HHG feature of the Mott insulator using the nonequilibrium dynamical-mean field theory [1]. We show the HHG spectrum qualitatively changes depending on the field strength, reflecting the itinerant or localized nature of the doublon-holon pairs. We also show that the HHG feature is not directly related to the dispersions observed in the single-particle spectrum unlike in semiconductors. Secondly, to reveal the relation between HHG and many body elemental excitations, we study the one-dimensional system [2]. We show that the semi-classical three step model combined with the elemental excitations works well to describe the HHG process. Finally, we study the effects of strong spin-charge couplings on HHG, which becomes important in higher dimensions than one [3]. We show that the spin-charge coupling leads to intriguing temperature (or band-gap) dependence of HHG as has been reported in the experiment on a Mott insulator Ca₂RuO₄ [4]. Our results suggest the potential application of HHG to detect many-body excitations, and possibility to find intriguing HHG behavior in SCESs.