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Quantum recoil in free-electron interactions with atomic lattices


The emission of light from charged particles underlies a wealth of scientific phenomena and technological applications. Classical theory determines the emitted photon energy by assuming an undeflected charged particle trajectory. In 1940, Ginzburg pointed out that this assumption breaks down in quantum electrodynamics, resulting in shifts—known as quantum recoil—in outgoing photon energies from their classically predicted values. Since then, quantum recoil in free-electron light-emission processes, including Cherenkov radiation and Smith–Purcell radiation, has been well-studied in theory, but an experimental demonstration has remained elusive. Here we present an experimental demonstration of quantum recoil, showing that this quantum electrodynamical effect is not only observable at room temperature but also robust in the presence of other electron-scattering mechanisms. By scattering free electrons off the periodic two-dimensional atomic sheets of van der Waals materials in a tabletop platform, we show that the X-ray photon energy is accurately predicted only by quantum recoil theory. We show that quantum recoil can be enormous, to the point that a classically predicted X-ray photon is emitted as an extremely low-energy photon. We envisage quantum recoil as a means of precision control over outgoing photon and electron spectra, and show that quantum recoil can be tailored through a host of parameters: the electron energy, the atomic composition and the tilt angle of the van der Waals material. Our results pave the way to tabletop, room-temperature platforms for harnessing and investigating quantum electrodynamical effects in electron–photon interactions.

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Fig. 1: Quantum recoil and multimode X-ray generation in Smith–Purcell radiation.
Fig. 2: Quantum recoil for free electrons interacting with graphite and hexagonal boron nitride, respectively.
Fig. 3: Tuning quantum recoil in Smith–Purcell radiation.

Data availability

The data represented in Figs. 13 are available as Supplementary Information files. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

All code that support the plots within this paper are available from the corresponding authors upon reasonable request.


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We thank A. Lim, Y. Y. Tay and I. Kaminer for helpful discussions. This project was partially supported by the National Research Foundation (Project ID NRF2020-NRF-ISF004-3525) and the Agency for Science, Technology and Research (A*STAR) Science & Engineering Research Council (Grant No. A1984c0043). We acknowledge the Facility for Analysis, Characterisation, Testing and Simulation, Nanyang Technological University, Singapore, for use of their electron microscopy/X-ray facilities. Z.L. acknowledges the support from National Research Foundation, Singapore, under its Competitive Research Programme (CRP) (NRF-CRP22-2019-0007 and NRF-CRP26-2021-0004). This research is also supported by A*STAR under its AME IRG Grant (Project No. A2083c0052). L.J.W. acknowledges the Nanyang Assistant Professorship Start-up Grant.

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Authors and Affiliations



S.H. led the project, designed and performed the electron microscopy experiments and analysed the data. R.D. and Z.L. prepared the samples. N.P. and S.H. developed the theory and performed the simulations. J.S.H. and C.B. contributed to the analysis of the experimental results. S.H. and L.J.W. wrote the paper, with inputs from all other authors. L.J.W. conceived the idea and supervised the project.

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Correspondence to Liang Jie Wong.

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Nature Photonics thanks Peter Baum 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 Sections 1–11.

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Source Data Fig. 2

Source data for Fig. 2.

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Huang, S., Duan, R., Pramanik, N. et al. Quantum recoil in free-electron interactions with atomic lattices. Nat. Photon. 17, 224–230 (2023).

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