Abstract We study effects of lattice imperfections on high-harmonic generation from correlated systems using the Fermi–Hubbard model. We simulate such imperfections by randomly modifying the chemical potential across the individual lattice sites. We control the degree of electron–electron interaction by varying the Hubbard U. In the limit of vanishing U, this approach results in Anderson localization. For nonvanishing U, we rationalize the spectral observations in terms of qualitative k-space and real-space pictures. When the interaction and imperfection terms are of comparable magnitude, they may balance each other out, causing Bloch-like transitions. If the terms differ significantly, each electron transition requires a relatively large amount of energy and the current is reduced. We find that imperfections result in increased high-harmonic gain. The spectral gain is mainly in high harmonic orders for low U and low orders for high U.
Using the one-dimensional Fermi-Hubbard model we study the effects of lattice imperfections on high-harmonic generation (HHG) from correlated systems. We simulate such imperfections by randomly modifying the chemical potential across the individual lattice sites. We control the degree of correlation by varying the Hubbard
U. In the limit of vanishing
U, this approach results in Anderson localization. For non-vanishing
U, we explain the spectral observations using a qualitative picture in which correlation and the imperfections may balance each other out, causing Bloch-like transitions, i.e., transitions similar to those occurring in the case with small or vanishing
U and with vanishing imperfection-induced energy gaps, even though the dynamics take place under conditions of high
U and severe imperfections. We verify this picture by studying HHG spectra where imperfections are found to cause gain in the HHG spectra. The spectral gain is mainly in high harmonic orders for low correlation and low harmonic orders for high correlation. We explain this using the following qualitative picture. For low correlation, the addition of imperfections gives rise to significant energy gaps in the system, corresponding to high harmonics, and when the correlation is massive the addition of imperfections balances out the correlation, resulting in smaller energy gaps, meaning lower harmonic orders. We further demonstrate how in the unbalanced cases, i.e., high
U and relatively small amount of imperfection or vice versa, the dynamics are largely adiabatic, and how in the balanced cases, with similar magnitude of correlation and imperfection, the dynamics are qualitatively similar.
Using the one-dimensional Hubbard model, which is commonly used for describing, e.g., high-
Tc superconducting cuprates, we study high-harmonic generation (HHG) from doped, correlated materials. Doping is modeled by changing the number of electrons in the lattice from the conventional half-filling case. For relatively small Hubbard
U, i.e., small electron-electron correlation, we find little to no effect of doping on the dynamics and the HHG spectra. For increasing
U the degree of doping has a marked effect on the dynamics and spectra. We explain these findings through the quasiparticle-based doublon-holon picture. The dynamics are separated into two types, first, doublon and holon movement, and, second, doublon-holon pair creation and annihilation. Doping results in all configurations containing doublons or holons. Those quasiparticles can move at no extra cost in energy regardless of the correlation level. This motion at no energy cost increases the high-harmonic gain for low- and medium-harmonic orders. We discuss that in the high-
U limit, antiferromagnetic ordering becomes increasingly unlikely with increasing doping rates and explain an associated drop in the high-order harmonics relative to the case of half-filling.
Using the Hubbard model we study how the process of high-order harmonic generation (HHG) is modified by electron-electron correlation for both finite and bulk systems. A finite-size enhancement of the HHG signal is found and attributed to electrons backscattering off the lattice edges. Additionally, with the increasing strength of the electron-electron correlation an enhancement of the high-frequency regime of the HHG spectrum is found. This is attributed to the on-site Coulomb repulsion between electrons giving rise to a localized correlation-induced quiver motion of the electrons. The finite-lattice enhancement dominates the HHG spectra from a few harmonic orders until a threshold from which the correlational enhancement dominates. This threshold is determined by the degree of correlation and decreases into the low-frequency regime for increasing electron-electron correlation. This infers that as the electron-electron correlation increases, the finite-size effect on the electron dynamics decreases.
The key optical and electronic functionalities in condensed materials are determined by the band filling of electrons and their Coulomb correlations. To directly capture how many-body correlations influence the correlated electron dynamics under the driving of laser pulses, the comprehensible quasiparticle picture is desired to distinguish the ultrafast creation and annihilation of doublon-holon pairs in attosecond timescale. Here, we adopt the one-dimensional non-half-filling Hubbard model to study the high-harmonic generation (HHG) in correlated electron systems. As the value of Hubbard
U increases, the cutoff energy and spectral features in HHG spectra have been revealed and their scaling laws are explained by the characteristic energy gaps obtained from the electronic bands under the quasiparticle picture. The adjustable degree of band filling in correlated systems paves a way to enhance high-harmonic emissions by regulating the creation of doublon-holon pairs. The complex temporal profile of HHG is elucidated in this work by the light-induced evolution of quasiparticle bands in correlated materials. In addition, the dephasing of the HHG spectrum caused by the vibration-induced disorder or lattice temperature is affirmed in the correlated electron systems and this dephasing process is attributed to quasiparticle-lattice scattering during the doublons and holons propagating among the disordered lattice sites.
The spectra produced by high-order harmonic generation (HHG) typically exhibit well-defined peaks at odd integers times the laser frequency. However, in recent investigations of HHG from correlated materials, spectra exhibit signals at noninteger harmonics which do not conform to the well-known symmetry-based selection rules for HHG spectra. Here, we use the Fermi-Hubbard model to study HHG from a linear chain of atoms. This model allows us to study both the correlated and uncorrelated phases through a specification of the amount of onsite electron-electron repulsion. The presence of signal at noninteger harmonics can be interpreted as originating from the population of multiple Floquet states. We show how this coupling to different Floquet states depends on the characteristics of the driving pulse and the strength of the electron-electron interaction in the system.
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. [1]