High Harmonic Generation in Strongly Correlated Systems
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In recent years, the study of phenomena pertaining to non-linear properties of materials has seen a major upswing - especially in the context of High Harmonic Generation (HHG). In this thesis, an account of the current state of research in this area will be given. In addition, we seek to combine two seemingly disparate areas of research, both of which have been the subject of numerous years of intense research - namely those of HHG in solid state materials, and the optical response of strongly correlated quantum systems. To this end we will rely on solving the Fermi-Hubbard model coupled to an electromagnetic field under time propagation. With the aid of both numerical work and simple energy level analyses, we are able to explain most of the characteristics of our calculated spectra. High field strength will induce a Mott insulator to metal phase transition whose imprints will be established through time resolved high harmonic emission and doublon and spin correlation functions. The various HHG spectra, together with said correlation functions will be studied through an Exact diagonalization algorithm in conjunction with an Arnoldi-Lanczos time propagator. The parameter space considered is comprised of the electron-electron repulsion energy, U, and peak electric field strength. Additionally, the study is not restricted to half-filling, and results for doped materials will be presented. We find that the high U-induced energy gap in the Fermi-Hubbard model plays the same role as the valence-conduction bandgap in models like for instance the Semiconductor Bloch Equations when it comes to generating high harmonic radiation through multiphoton processes. The central part of this thesis aims at providing insight to and making further contributions to an article published in Nature Photonics in March 2018.