Abstract
Electrons, phonons and photons are three particles or quasiparticles whose interactions and related elementary excitations are essential for understanding complex phenomena in condensed-matter physics. Paradigmatic examples include polarons arising from electron–phonon interactions and polaritons, from photon–phonon interactions. However, the overall excitation of direct coupling among the three has not been explored in experiments owing to significant mismatches in their energy and momentum scales. Here we realize steady-state electron‒phonon‒photon excitation via integrated lasing radiation and nonlinear conversion within a single crystal. Via our cavity design, we suppress strong spontaneous emission oscillation and realize weak multiphonon-coupled lasing, in which coherent phonons are created as energy offsets between electrons and photons. These dynamic phonons can self-adaptively heterodyne to generate the momentum required for the intracavity photon nonlinearity by selectively blocking the fundamental-wave laser. As evidence, we observe not only efficient and ultrabroadband continuous-wave second-harmonic generation in arbitrary directions but also flexible micrometre periodic lattice modulations induced by the heterodyning of inherent phonons with nanometre-scale wavelengths. This case represents simultaneous energy and momentum matching in a steady nonlinear lasing process.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China via grant numbers 52422201 (F.L.), 52025021 (H.Y.), 92463304 (H.Z.), 92163207 (H.Z.), U23A20558 (H.Y.), 52372010 (F.L.) and 92363001 (Y.-F.C.); National Key Research and Development Program of China via grant numbers 2021YFB3601504 (H.Z.), 2023YFF0718801 (F.L.) and 2021YFA0717800 (F.L.); Natural Science Foundation of Shandong Province via grant number ZR2023ZD53 (F.L.). F.L. acknowledges H. Si and Y. Zhou for support with the laser experiments. F.L. acknowledges D. Lu and Y. Fu for support with the fluorescence measurements. F.L. acknowledges Y. Zhao and K. Wu for helpful discussions.
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H.Y. and H.Z. conceived and supervised the project. F.L. and C.H. performed the crystal design, cavity coating and laser experiments. Y.-F.C. provided the theoretical analysis for electron–phonon–photon-coupled nonlinear laser. All authors contributed to the discussion and preparation of the paper.
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Nature Physics thanks Anton Husakou and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Supplementary Figs. 1–15, Tables 1–4 and Discussion.
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Source Data Fig. 3
Source data for the laser spectrum and piezoelectric measurements.
Source Data Fig. 4
Source data for the laser spectrum.
Source Data Fig. 5
Source data for the fluorescence spectrum and laser powers.
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Liang, F., He, C., Yu, H. et al. Electron‒phonon‒photon excitation in steady nonlinear lasing. Nat. Phys. 21, 1905–1910 (2025). https://doi.org/10.1038/s41567-025-03079-1
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DOI: https://doi.org/10.1038/s41567-025-03079-1
