High-order harmonic generation (HHG) from solid-state semiconductors drops sharply under long-wavelength infrared laser pulses. By combining mid-infrared spectroscopy with quantum calculations, researchers sought to understand why this happens, ultimately finding strong evidence that electron-lattice interactions reduce efficiency.
Study: Strong field spectroscopy of many-body interactions in solids. Image Credit: GarryKillian/Shutterstock.com
This research, published in Nature Communications, explains how electron dynamics affect light emission under intense optical fields and helps understand how light interacts with solid materials.
Advancements in Nonperturbative Light Generation
HHG converts laser light into higher-frequency light, producing extreme-ultraviolet (XUV) radiation and attosecond-long pulses. Although originally developed in atomic gases, HHG in solid materials offers a pathway to build compact light sources and advanced optical tools. In solids, intense laser pulses drive electrons through the crystal’s energy bands, thereby creating electron-hole pairs that emit light as they interact.
However, interactions within the crystal can disrupt the coordinated motion of electrons and holes, reducing the emitted light's intensity. Earlier models relied on dephasing times of only a few femtoseconds to explain experimental results, despite coherence in semiconductors lasting tens of femtoseconds under weaker optical fields. The origins of this rapid loss of coherence remain an open question in solid-state optics.
Atomically Thin Semiconductors Reveal Coherence Loss
Researchers comprehensively explored atomically thin tungsten disulfide (WS2) and molybdenum disulfide (MoS2), alongside 140 nm-thick
polycrystalline cadmium selenide (CdSe) films, to understand why electron coherence fades rapidly in solids. The thin samples helped limit optical distortions caused by light traveling through the material.
The experiments utilized a titanium-sapphire laser system operating at 800 nm with 35-femtosecond pulses and a repetition rate of 1 kHz. An optical parametric amplifier and a noncollinear difference-frequency generation unit produced tunable mid-infrared pulses spanning 3–12 μm, with the high-harmonic generation measurements conducted between approximately 3 and 5 μm.
Laser intensities reached 1.5 terawatts per square centimeter. The emitted harmonics were collected in transmission and then measured using an imaging spectrometer equipped with a UV-enhanced detector.
For analysis, the study combined first-principles calculations with semiconductor Bloch equations to investigate electron motion and its interaction with lattice vibrations. Density functional theory (DFT) and density functional perturbation theory (DFPT) calculations were performed using Quantum ESPRESSO.
The EPW software was employed with localized Wannier functions to calculate momentum-dependent electron-phonon scattering rates. The results were then added into a three-band tight-binding model that included spin-orbit coupling.
The Mechanisms Behind Femtosecond Dephasing
The experiments showed that high-order harmonic emission decreased sharply as the driving laser wavelength increased. The measured emission followed a power-law decline, with scaling exponents ranging from nearly λ-6.2 to λ-8.9 across WS2, MoS2, and CdSe. This decline was significantly steeper than the typical λ-4 scaling observed in atomic gases.
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Changing the laser intensity by more than 70% altered the scaling exponents by less than 10%, suggesting that carrier multiplication and electron-electron collisions were not the main contributors to the observed dephasing. Researchers traced the effect to changes in electron–phonon scattering across the crystal’s momentum space. Near the band extrema, electron scattering times were approximately 70–100 femtoseconds.
As the laser field accelerated electrons into other regions of the Brillouin zone, scattering became faster, and local dephasing times fell to around two to four femtoseconds. By adding these scattering rates into the semiconductor Bloch equations, the team successfully reproduced both the steep decline in harmonic emission and the observed interference patterns.
The calculations yielded an effective coherence time of about four femtoseconds along electron trajectories, providing a fundamental explanation for the rapid loss of coherence.
Implications for Optical Device Development
These findings could help scientists improve solid-state sources of XUV light, frequency combs, and attosecond pulses, which are currently limited by low conversion efficiency. Understanding how electron-phonon scattering reduces coherence provides a basis for selecting semiconductors with weaker electron-phonon interactions and adjusting crystal structures to control lattice vibrations.
In quantum photonics, solid-state HHG can produce nonclassical light, including multimode squeezed states and entangled photons. Preserving electron-hole coherence is key for generating these quantum states.
Techniques such as cryogenic cooling and phononic bandgap engineering could mitigate the effects of lattice vibrations, supporting the development of bright, compact quantum light sources for integrated optical and quantum information systems.
Future Directions for Coherence Engineering in Solids
This research explores why electron coherence can last only a few femtoseconds during HHG in solids. The rapid loss of coherence arises from electron–phonon scattering as electrons traverse regions of the crystal where scattering is stronger.
This explanation reduces reliance on assumed dephasing times and helps bridge the gap between weak-field semiconductor optics and strong-field behavior.
Future research could explore strain engineering, temperature control, and coherent excitation of lattice vibrations to reduce scattering. Cryogenic cooling and specially designed two-dimensional heterostructures may also extend coherence times and increase harmonic output. Overall, these approaches could pave the way for developing more efficient solid-state XUV sources and compact quantum photonic devices.
Journal Reference
Korolev, V., et al. (2026). Strong field spectroscopy of many-body interactions in solids. Nature Communications, 17. DOI: 10.1038/s41467-026-78716-1, https://www.nature.com/articles/s41467-026-78716-1.
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