Optical Distinguishability of Mott Insulators in Time vs Frequency Domain

TL;DR

This paper investigates how the optical response of Mott insulators in high harmonic generation varies with system parameters, revealing that time domain measurements offer better distinguishability than frequency domain, especially at high lattice spacings and field strengths.

Contribution

The study introduces an analytical framework and numerical simulations to analyze the distinguishability of Mott insulators in HHG, highlighting the advantages of time domain analysis over frequency domain.

Findings

Reduced distinguishability of Mott insulators at high lattice spacing and field strength.

Time domain measurements outperform frequency domain in resolving Mott insulators.

Conductors become more distinguishable in the frequency domain at high parameter g.

Abstract

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