Optical distinguishability of Mott insulators in the time versus frequency domain

High Harmonic Generation (HHG) promises to provide insight into ultrafast dynamics and has been at the forefront of attosecond physics since its discovery. One class materials that demonstrate HHG are Mott insulators whose electronic properties great interest given their strongly-correlated nature. Here, we use paradigmatic representation insulators, half-filled Fermi-Hubbard model, investigate potential using response distinguish these materials. We develop an analytical argument based on Magnus expansion approximation evolution by Schrodinger equation indicates decreased distinguishability as lattice spacing, $a$, strength driving field, $F_0$, increase relative frequency, $\omega_0$. This is then bolstered through numerical simulations different systems subsequent comparison responses in both time frequency domain. Ultimately, reduced resolution domains when dimensionless parameter $g \equiv aF_0 / \omega_0$ large, though domain provides higher distinguishability. Conductors exempted from trends, becoming much more distinguishable high $g$.