Solid-state high-harmonic generation (HHG) has emerged as a powerful probe for nonequilibrium quantum many-body dynamics in condensed matter systems. In weakly correlated materials, the nonlinear optical response underlying HHG can often be described within a single-particle framework using the time-dependent Schrödinger equation (TDSE) or semiconductor Bloch equations. In such approaches, decoherence effects are usually incorporated phenomenologically through a dephasing time T_2, which successfully reproduces several experimental features such as harmonic plateaus and cutoff energies. However, this phenomenological treatment encounters fundamental limitations in strongly correlated systems, including Mott insulators, where electron—electron interactions dominate the underlying dynamics. In conventional TDSE simulations, the parameter T_2 is typically introduced ad hoc to mimic scattering processes, making it difficult to distinguish genuine many-body decoherence—originating from electron—electron or electron—phonon interactions—from numerical artifacts.
To overcome these limitations, this work investigates HHG in a strongly correlated system described by a one-dimensional half-filled Fermi—Hubbard model with L=12 lattice sites and nearest-neighbor hopping amplitude t_0=0.52\,\mathrmeV. The system is driven by an intense mid-infrared laser pulse characterized by a \sin^2 envelope, a central wavelength of 9110\,\mathrmnm, and a duration of 16 optical cycles. Two complementary theoretical approaches are employed. First, the nonequilibrium dynamics of the closed quantum system are simulated using the time-dependent Schrödinger equation, where the many-body wave function is propagated numerically using the Crank—Nicolson scheme to ensure stable unitary evolution. Second, to explicitly account for environmental decoherence, the system is treated as an open quantum system described by a density-matrix formalism governed by the Lindblad master equation. In this framework, many-body dephasing channels are incorporated through Lindblad operators, and the time evolution of the density matrix is solved using a fourth-order Runge—Kutta method. The high-harmonic spectra are obtained from the Fourier transform of the time-dependent current expectation value, while the doublon number, defined as the expectation value of the double-occupancy operator, is used to characterize correlation-driven electronic excitations.
Comparative calculations are first performed in the absence of dephasing (T_2=\infty) to benchmark the consistency of the two approaches. The results show excellent agreement between the TDSE and the density-matrix master equation in both the high-harmonic spectra and the time evolution of the doublon number. Under weak-field driving (F_0=10\,\mathrmMV/cm), the harmonic spectra are dominated by low-order harmonics with rapidly decaying intensity, while the doublon number remains nearly constant within the range of 0.150—0.162. This agreement confirms the numerical equivalence of the two theoretical frameworks in the coherent limit and validates the reliability of the open-system approach.
When finite dephasing is introduced, significant modifications to the high-harmonic spectra are observed. In particular, dephasing strongly suppresses long-lived interband coherent noise, resulting in sharper harmonic peaks and a more pronounced plateau structure, especially under strong-field driving (F_0=50\,\mathrmMV/cm). Notably, while the spectral contrast and harmonic yield are strongly influenced by decoherence, the cutoff energy remains largely unchanged, indicating that it is mainly determined by intrinsic energy scales such as the Mott gap and the external field strength.
Further analysis of doublon dynamics reveals that dephasing accelerates the formation of doublons. In the absence of dephasing, doublon excitation begins at approximately t\approx-4 optical cycles. When strong dephasing (T_2=10\,\mathrmfs) is introduced, the onset shifts to around t\approx-7 optical cycles and the growth rate becomes significantly larger. This behavior originates from the decoherence-induced weakening of long-range quantum correlations, which otherwise suppress electronic transitions through quantum interference effects. By shortening the coherence lifetime of quantum states, dephasing facilitates nonadiabatic tunneling and multiphoton excitation processes, thereby accelerating doublon generation.
To further elucidate the emission mechanism, a time-frequency analysis based on the Gabor transform is performed. The spectrogram reveals two distinct quantum trajectories analogous to the short and long trajectories in the semiclassical three-step model of HHG. In the absence of dephasing, both trajectories contribute to the emission and produce clear interference patterns. When strong dephasing is introduced, the contribution from the long trajectory is strongly suppressed, while the short trajectory remains dominant. This occurs because long trajectories involve longer electron—hole propagation times and are therefore more sensitive to environmental perturbations, whereas short trajectories accumulate less phase and are more robust against decoherence. This mechanism leads to a distinctive orbital filtering effect, in which decoherence selectively suppresses phase-sensitive quantum pathways while preserving the dominant short-trajectory emission.
In summary, this work provides a systematic theoretical investigation of dephasing effects on high-harmonic generation in strongly correlated systems. By combining TDSE simulations with a Lindblad-form open-system framework, the study establishes a rigorous methodology for incorporating many-body decoherence into HHG simulations. The results demonstrate that dephasing not only modifies the spectral characteristics of harmonic emission but also reshapes the underlying quantum-path interference and excitation dynamics. In particular, the discovery of the decoherence-induced orbital filtering mechanism highlights the possibility of controlling HHG emission through engineered environmental interactions. These findings provide new insights into the interplay between coherence and dissipation in nonlinear optical processes of correlated materials and offer a theoretical basis for optimizing high-harmonic sources and achieving coherent control in quantum many-body systems.