Effects of lattice imperfections on high-harmonic generation from correlated systems

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.