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arXiv:2610.12136

Dynamical many-body control of high harmonic generation in a Mott insulator

Mingyao Guo, Ryo Noguchi, Mohammad Muntasir Hassan, Steven J. Gomez Alvarado, Reina Gomez, Yao-Jui Chan, Yu-Chieh Wen, Stephen D. Wilson, Yao Wang, David Hsieh

Published Oct 8, 2026• 0 citations
arXivHTMLPDF

Abstract

High harmonic generation (HHG) has emerged as a powerful probe of ultrafast electron dynamics in solids. However, in strongly correlated materials, where electronic excitations arise from many-body interactions rather than single-particle band dispersion, the field remains in its infancy. Here, we report HHG up to the 23$^{rd}$ order in the prototypical Mott insulator La$_2$CuO$_4$. We observe a robust 4 eV cutoff that is independent of driving field strength, revealing an intrinsic energy scale defined by the Hubbard bands. Using time-resolved high harmonic spectroscopy, we disentangle the distinct contributions of carrier creation, intraband acceleration, and interband recombination to the nonequilibrium radiation spectrum. We demonstrate that photo-doping triggers a fundamental reorganization of the many-body manifolds above a critical excitation density, a process that renormalizes the band curvature and suppresses nonlinear intraband currents, thereby directly imprinting the signature of many-body band reconstruction onto the harmonic emission. These results establish HHG as a sensitive probe of subtle correlation-driven electronic reconstructions and highlight that many-body interactions enable extreme nonlinear optical responses that are highly tunable in nonequilibrium states.

DOI
10.48550/arxiv.2610.12136

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High harmonic generation (HHG) has emerged as a powerful probe of ultrafast electron dynamics in solids. However, in strongly correlated materials, where electronic excitations arise from many-body interactions rather than single-particle band dispersion, the field remains in its infancy. Here, we report HHG up to the 23rd^{rd}rd order in the prototypical Mott insulator La2_22​CuO4_44​. We observe a robust 4 eV cutoff that is independent of driving field strength, revealing an intrinsic energy scale defined by the Hubbard bands. Using time-resolved high harmonic spectroscopy, we disentangle the distinct contributions of carrier creation, intraband acceleration, and interband recombination to the nonequilibrium radiation spectrum. We demonstrate that photo-doping triggers a fundamental reorganization of the many-body manifolds above a critical excitation density, a process that renormalizes the band curvature and suppresses nonlinear intraband currents, thereby directly imprinting the signature of many-body band reconstruction onto the harmonic emission. These results establish HHG as a sensitive probe of subtle correlation-driven electronic reconstructions and highlight that many-body interactions enable extreme nonlinear optical responses that are highly tunable in nonequilibrium states.
High-harmonic generation (HHG) in strongly correlated Mott insulators is investigated using exact diagonalization and time-dependent density-matrix propagation of a laser-driven one-dimensional Hubbard chain. By projecting onto equilibrium Hubbard bands, we use the doublon population and its dynamics as a diagnostic to analyze intraband (spin-wave-like) and interband (doublon-holon creation) excitation channels. A filling-dependent crossover emerges: Bloch-like intraband response at dilute filling, mixed dynamics at intermediate filling, and interband-dominated HHG with plateau and cutoff near half filling. In the considered parameter range, increasing interaction strength UUU strongly suppresses interband contributions through the enlarged Mott gap and correlation-induced localization. Intra- and interband current decomposition reveals opposing flows below the Mott gap (Δ_{\mathrm{Mott}}) and selective dephasing suppression of interband coherence, enhancing net doublon accumulation. Time-frequency analysis uncovers the filling-dependent features of quantum trajectories, manifesting in distinct below-Δ_{\mathrm{Mott}} emission. This doublon-based analysis provides a transparent link between equilibrium spin-charge separation and nonequilibrium strong-field response, and clarifies how dephasing modifies interband coherence and doublon accumulation.
We study high-harmonic generation (HHG) in the one-dimensional Hubbard model in order to understand its relation to elementary excitations as well as the similarities and differences to semiconductors. The simulations are based on the infinite time-evolving block decimation (iTEBD) method and exact diagonalization. We clarify that the HHG originates from the doublon-holon recombination, and the scaling of the cutoff frequency is consistent with a linear dependence on the external field. We demonstrate that the subcycle features of the HHG can be reasonably described by a phenomenological three step model for a doublon-holon pair. We argue that the HHG in the one-dimensional Mott insulator is closely related to the dispersion of the doublon-holon pair with respect to its relative momentum, which is not necessarily captured by the single-particle spectrum due to the many-body nature of the elementary excitations. For the comparison to semiconductors, we introduce effective models obtained from the Schrieffer-Wolff transformation, i.e., a strong-coupling expansion, which allows us to disentangle the different processes involved in the Hubbard model: intraband dynamics of doublons and holons, interband dipole excitations, and spin exchanges. These demonstrate the formal similarity of the Mott system to the semiconductor models in the dipole gauge, and reveal that the spin dynamics, which does not directly affect the charge dynamics, can reduce the HHG intensity. We also show that the long-range component of the intraband dipole moment has a substantial effect on the HHG intensity, while the correlated hopping terms for the doublons and holons essentially determine the shape of the HHG spectrum. A new numerical method to evaluate single-particle spectra within the iTEBD method is also introduced.
Competition and cooperation among orders is at the heart of many-body physics in strongly correlated materials and leads to their rich physical properties. It is crucial to investigate what impact many-body physics has on extreme nonlinear optical phenomena, with the possibility of controlling material properties by light. However, the effect of competing orders and electron-electron correlations on highly nonlinear optical phenomena has not yet been experimentally clarified. Here, we investigated high-order harmonic generation from the Mott-insulating phase of Ca_{2}RuO_{4}. Changing the gap energy in Ca_{2}RuO_{4} as a function of temperature, we observed a strong enhancement of high order harmonic generation at 50 K, increasing up to several hundred times compared to room temperature. We discovered that this enhancement can be well reproduced by an empirical scaling law that depends only on the material gap energy and photon emission energy. Such a scaling law can hardly be explained by the electronic structure change in the single particle model and has not been predicted by previous theoretical studies on HHG in the simple Mott-Hubbard model. Our results suggest that the highly nonlinear optical response of strongly correlated materials is influenced by competition among the multiple degrees of freedom and electron-electron correlations.
Solid-state high-harmonic spectroscopy is becoming an emerging tool for probing nonequilibrium many-body dynamics. Yet, direct measurements of strongly driven, sub-optical-cycle dynamics in correlated materials during high-harmonic emission remain largely unexplored. Here, we measure high-harmonic emission chirp in a prototypical one-dimensional Mott insulator, which encodes strongly driven doublon-holon dynamics at sub-optical-cycle timescales. We observe a positive chirp for above band gap harmonics, indicating that high harmonics are dominated by doublon-holon recombinations. We further show a harmonic order-dependent dephasing, which can be understood through different doublon-holon excursion distances associated with each harmonic. These results reveal coherent doublon-holon dynamics and their ultrafast dephasing in Mott insulators, which is relevant to other nonequilibrium light-induced phenomena, such as Floquet engineering.
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]
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 UUU 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.