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Optics Express

Theoretical investigation of momentum-dependent carrier-carrier scattering from crystal-strong laser interaction

Yan Shi, Ye Gu, Shuai Chang, Shoufeng Tong, Xi Zhao

Published Apr 29, 2026• 0 citations
Publisher

Abstract

Ultrafast electron–electron scattering is widely believed to dominate coherence loss in strongly driven solids, yet its microscopic, momentum-resolved description under intense laser excitation remains lacking. In current solid-state high-harmonic generation (HHG) modeling, the dephasing time T 2 is typically introduced phenomenologically, without a field-dependent many-body derivation. Here we develop a first-principles microscopic theory of carrier–carrier scattering in strongly field–driven crystalline solids. Starting from a Born–Markov quantum master equation in the Houston–Floquet basis, we derive a field-dressed Fermi’s golden rule for the momentum-resolved dephasing rate Γ( k ), in which the driving laser field explicitly modifies scattering matrix elements, occupation factors, screening, and energy conservation. We demonstrate that the rapid formation of a nonequilibrium carrier plasma under mid-infrared excitation dramatically enhances electron–electron scattering through phase-space expansion and Floquet-dressed Coulomb interactions, rendering it the dominant dephasing channel while electron–phonon scattering remains comparatively weak. This microscopic framework quantitatively explains the few-femtosecond coherence times universally extracted from HHG experiments. Finally, we show that the full momentum-dependent decoherence kernel, Γ( k ), can be reconstructed from measured HHG spectra, thereby establishing solid-state HHG as a nonlinear spectroscopy of ultrafast many-body scattering in solids.

DOI
10.1364/oe.599101

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Ultrafast electron–electron scattering is widely believed to dominate coherence loss in strongly driven solids, yet its microscopic, momentum-resolved description under intense laser excitation remains lacking. In current solid-state high-harmonic generation (HHG) modeling, the dephasing time T 2 is typically introduced phenomenologically, without a field-dependent many-body derivation. Here we develop a first-principles microscopic theory of carrier–carrier scattering in strongly field–driven crystalline solids. Starting from a Born–Markov quantum master equation in the Houston–Floquet basis, we derive a field-dressed Fermi’s golden rule for the momentum-resolved dephasing rate Γ( k ), in which the driving laser field explicitly modifies scattering matrix elements, occupation factors, screening, and energy conservation. We demonstrate that the rapid formation of a nonequilibrium carrier plasma under mid-infrared excitation dramatically enhances electron–electron scattering through phase-space expansion and Floquet-dressed Coulomb interactions, rendering it the dominant dephasing channel while electron–phonon scattering remains comparatively weak. This microscopic framework quantitatively explains the few-femtosecond coherence times universally extracted from HHG experiments. Finally, we show that the full momentum-dependent decoherence kernel, Γ( k ), can be reconstructed from measured HHG spectra, thereby establishing solid-state HHG as a nonlinear spectroscopy of ultrafast many-body scattering in solids.
Real-time time-dependent density functional theory provides a first-principles description of coherent electron dynamics in laser-driven solids, but its unitary formulation cannot capture the irreversible scattering, relaxation, and decoherence processes that drive excited carriers toward equilibrium. Here, we develop a dissipative rt-TDDFT framework in which first-principles electron-phonon interactions enter the evolution of the reduced one-body density matrix through self-energy-derived collision integrals within the Born-Markov approximation. The approach retains the quantum-coherent real-time propagation of the electronic system while introducing phonon-mediated transitions that redistribute carriers in energy and crystal momentum, thereby incorporating the microscopic momentum-transfer processes responsible for relaxation in real materials. The resulting framework provides a practical first-principles route to simulate relaxation, decoherence, and time-resolved spectroscopic signatures in realistic crystalline materials.
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.
Time-dependent density functional theory (TDDFT) has developed into an efficient and versatile description of realistic extended many-electron systems driven, e.g., by strong laser fields. It accounts for the fully coherent evolution of the NNN-electron wave packet representing an isolated system. Decoherence as encountered in open systems by coupling to external degrees of freedom of a bath of, e.g., phonons or defects, is, by construction, absent. In this work we present an open-quantum system (OQS) extension of TDDFT accounting for dephasing and decoherence due to electron-phonon or defect scattering. We test the OQS-TDDFT for high-harmonic generation and irreversible changes of dielectric properties in solids driven by strong ir and mid-ir laser pulses. We present applications to diamond as a prototypical wide band-gap dielectric. For weak pulses we demonstrate the equivalence of OQS-TDDFT with the solution of the Bloch equations for the reduced one-particle density matrix while differences appear at high excitation densities. Our study highlights the importance of the accurate representation of the band structure in simulations of the harmonic spectrum. Narrow avoided crossings within the Brillouin zone can give rise to Bloch-type oscillations.
ABSTRACT The physical origin of the ultrashort dephasing time T 2 (≈ O(1) fs), persistently addressed in the solid‐state high‐harmonic generation (HHG), remains an unresolved and challenging issue because the electron scattering at such a short timescale within solids is hardly identified. Here we investigate HHG of the 1D Hubbard model in the dissipative quantum environment within a frame of the Lindblad equation. In the study, in the limit of a small interatomic distance, we make the first verification of the solid‐state Dicke superradiance, the coherent stimulated emission triggered by the spontaneous emission, as well as the broadband emission mimicking the blackbody radiation due to the electron scattering in each harmonic multiple. Further, we find a strong destructive interference between the Dicke superradiance and the broadband emission, which makes a scale down of the effective electron scattering time and leads to just few‐femtosecond dephasing time T 2 . This finding explains a long‐standing problem of the ultrafast femtosecond electron dephasing in HHG. The present study could also serve as a pertinent platform for understanding the nonequilibrium dissipative dynamics of correlated electron systems.
The influence of carrier correlation processes on the interaction and propagation of femtosecond optical pulses in an inverted semiconductor is theoretically investigated. Microscopically treated Coulomb scattering described from a first-principles theory, including both diagonal and nondiagonal dephasing, is seen to cause considerably different behavior on the dynamics than that modeled by employing a rate-equation approximation. Semiconductor intrinsic optical nonlinearities such as gain saturation and adiabatic following, controlled by microscopic dephasing and relaxation mechanisms, manifest dominantly in ultrafast transient effects that, experimentally, can appear as a typical Kerr-type (instantaneous) nonlinearity. It is shown that one cannot invoke an adiabatic elimination for the polarization equation on femtosecond time scales. The present self-consistent theory successfully explains recent experimental measurements without recourse to parametrized equations. The possible role of non-Markovian relaxation is also discussed.
Ultrafast laser pulse has provided a systematic way to inspect the dynamics of electrons in condensed matter systems. In this paper, by means of time-dependent density matrix renormalization group, we study an ultrafast laser-driven Kondo lattice model, in which conduction electrons are strongly coupled with magnetically local moments. The single-particle spectral function due to strong correlation effects and photon emission in the nonequilibrium states under laser driving are calculated. We find laser field excited collective doublon-hole pairs and an associated transient melting of Kondo coherence phase, signifying the collapse of Kondo energy gap. Moreover, we show that the photon emission, induced by a strong laser field, exhibits a different intensity characteristics than in the equilibrium Kondo insulator, which could be explained by the Kondo collapse and related suppression of both intraband and interband contribution in Kondo melting liquid. This theoretical insight is accessible with time- and angle-resolved photoemission spectroscopy and high-harmonic generation spectroscopy and will stimulate the investigation of nonequilibrium dynamics and nonlinear phenomenon in heavy fermion systems.