Tracking doublon-holon dynamics in high-harmonic generation from Mott insulators

Abstract: 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 $U$ 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.

• The paper introduces doublon population as a diagnostic to distinguish intraband Bloch motion from interband doublon-holon excitation.
• Employing exact diagonalization and time-dependent density-matrix propagation, the study reveals a filling-dependent crossover from intraband to interband dynamics.
• Enhanced Coulomb repulsion and dephasing are shown to suppress interband HHG, offering new control pathways for ultrafast nonlinear optical responses.

Microscopic Analysis of Doublon-Holon Dynamics in High-Harmonic Generation from Mott Insulators

Overview

The paper "Tracking doublon-holon dynamics in high-harmonic generation from Mott insulators" (2605.01388) provides a rigorous study of HHG in strongly correlated electronic systems, focusing on the one-dimensional Hubbard chain driven by femtosecond laser fields. Employing exact diagonalization and time-dependent density-matrix propagation, the authors introduce the doublon population—a measure of on-site double occupancy—as a physically insightful diagnostic that distinguishes intraband spin-wave–like motion from interband doublon-holon excitation. The central thesis posits a filling-dependent crossover: Bloch-like intraband response dominates at dilute filling, mixed intra/interband dynamics emerge at intermediate filling, and near half filling the HHG spectrum is governed by interband processes, characterized by pronounced plateau and cutoff features. This work establishes a clear quantitative link between equilibrium spin-charge separation and nonequilibrium strong-field response, elucidating the suppression mechanisms of interband dynamics induced by increased Coulomb repulsion and the critical role of dephasing in modulating harmonic emission and doublon generation.

Hubbard Band Structure and Doublon Distribution

The equilibrium spectral-function analysis reveals distinct differentiation of spin and charge sectors, determined by the doublon expectation value of eigenstates. The lower Hubbard band is singly occupied, dominated by spin fluctuations, while the upper band carries enhanced doublon weight and manifests charge-density fluctuations. The Mott gap $\Delta_{\mathrm{Mott}}$ defines the energetic threshold for doublon-holon generation.

Figure 1: Quasiparticle dispersions in the equilibrium spectral function, color-coded by doublon expectation value; separation between the Hubbard bands constitutes the Mott gap $\Delta_{\mathrm{Mott}}$.

Filling strongly modulates the doublon content: at low filling, doublon weights are negligible; increased filling enhances multi-doublon configurations, observable as an ascending doublon expectation in the upper band.

Filling-Dependent Crossover in HHG Response

Time-resolved current and HHG spectra analysis across three representative filling levels—dilute (5%), intermediate (25%), and half-filled (50%)—demonstrate pronounced crossover dynamics:

• Dilute filling (5%): HHG spectra exhibit predominantly low-order harmonics from intraband Bloch motion, with current oscillations tracing the pulse envelope and virtually null doublon growth.
• Intermediate filling (25%): Mixed intra/interband dynamics arise, initiated by increased doublon-holon excitation (especially for lower $U$), with substantial enhancement in the harmonic yield.
• Half-filling (50%): Plateau formation and broadband high-frequency emission dominate, tracking rapid doublon number saturation and persistent recombination processes.

Spectral cutoff features and harmonic plateau intensity are directly correlated with effective doublon generation, as supported by strong numerical results on time-dependent doublon populations and current profiles.

Interaction-Driven Suppression and Intercurrent Decomposition

Increasing on-site Coulomb repulsion $U$—from $5t_0$ to $10t_0$—enlarges the Mott gap and enforces correlation-induced charge localization, systematically suppressing interband HHG channels and limiting doublon-holon creation. This establishes a quantitatively robust correlation blockade mechanism and shifts the emission behavior toward intraband dominance.

The authors decompose total current into intra- and interband contributions using band projection operators constructed from doublon-weight distributions. For the half-filled case with strong $U$, the harmonic intensities below $\Delta_{\mathrm{Mott}}$ are comparable for both current channels but flow in opposite directions—a physically significant result indicating nontrivial correlation effects in the lower band.

Figure 2: Decomposition of intra- and interband currents and time-dependent doublon population for half-filling with $U/t_0=10$; contrasting behaviors shown for scenarios with and without dephasing.

Role of Dephasing: Coherence Suppression and Doublon Accumulation

Introducing Lindblad-type pure-dephasing in the density-matrix evolution—parametrized by $T_2$—enables selective suppression of interband coherence. Finite dephasing drastically reduces high-harmonic plateau formation, yet yields increased net doublon accumulation, since population is prevented from coherently returning to the ground sector. Sub-Mott-gap harmonic peaks become sharper and signal-to-noise improves, a result attributed to alleviation of destructive intra-interband interference. The dual role of dephasing is thus firmly substantiated, both in suppressing coherence and in enhancing incoherent doublon generation.

Quantum Trajectory Analysis: Emergence and Suppression

Time-frequency analysis of HHG in the below-$\Delta_{\mathrm{Mott}}$0 spectral region demonstrates that filling governs quantum trajectory features. At dilute filling, emission traces Bloch oscillations with no discernible quantum trajectories; at half-filling, well-defined emission trajectories are seen, attributed to doublon-holon recombination.

Figure 3: Temporal emission characteristics in below-$\Delta_{\mathrm{Mott}}$1 region illustrating quantum trajectory features for dilute vs. half-filled cases.

Many-body blockade effects at high filling suppress long-range doublon motion, weakening trajectory features—a direct implication of the contrasting many-body nature of eigenstates compared to single-particle Bloch oscillations.

Implications and Prospects

This doublon-centered diagnostic framework provides a transparent bridge between equilibrium band structure and driven nonequilibrium dynamics in Mott materials. Experimentally, manipulation of filling, on-site interaction, and environmental decoherence offers viable pathways for controlling HHG yields and probing strong-field many-body physics via high-harmonic emission. Theoretical advancements informed by these results may inform precise engineering of nonlinear optical responses and quantum trajectory modulation in correlated systems.

Future work may extend to multi-dimensional Hubbard models, long-range interactions, inclusion of phononic/impurity-induced decoherence, and exploration of complex quantum trajectory dynamics via advanced spectroscopic protocols.

Conclusion

Through exact calculation and density-matrix strong-field simulations, this study demonstrates that doublon-holon dynamics are central to the filling-dependent crossover in HHG from Mott insulators, governing the transition from intraband-dominated emission at low filling to interband plateau formation at half-filling. Enhanced on-site interaction suppresses charge excitation and harmonic yield, while Lindblad dephasing restricts coherence and increases doublon generation. The methodologies and results meaningfully advance the microscopic understanding of nonlinear optical phenomena in correlated materials, cementing doublon population as a critical probe and control parameter for ultrafast strong-field studies.