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# Anomalous nonlinear X-ray Compton scattering

## Abstract

X-ray scattering is typically used as a weak linear atomic-scale probe of matter. At high intensities, such as produced at free-electron lasers, nonlinearities can become important, and the probe may no longer be considered weak. Here we report the observation of one of the most fundamental nonlinear X-ray–matter interactions: the concerted nonlinear Compton scattering of two identical hard X-ray photons producing a single higher-energy photon. The X-ray intensity reached 4 × 1020 W cm−2, corresponding to an electric field well above the atomic unit of strength and within almost four orders of magnitude of the quantum-electrodynamic critical field. We measure a signal from solid beryllium that scales quadratically in intensity, consistent with simultaneous non-resonant two-photon scattering from nearly-free electrons. The high-energy photons show an anomalously large redshift that is incompatible with a free-electron approximation for the ground-state electron distribution, suggesting an enhanced nonlinearity for scattering at large momentum transfer.

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## Acknowledgements

This work was supported primarily by the US Department of Energy (DOE), Office of Basic Energy Sciences (BES) and the Volkswagen Foundation. Portions of this research were carried out at the Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory. Preparatory measurements were carried out at the Stanford Synchrotron Radiation Lightsource (SSRL). Both LCLS and SSRL are Office of Science User Facilities operated for the US Department of Energy Office of Science by Stanford University. M.F. acknowledges support from the Volkswagen Foundation. M.K. was supported by the DOE Office of Science Graduate Fellowship Program. M.T. and J.C. were supported by the Division of Materials Sciences and Engineering, BES, DOE under contract 51 DE-AC02-76SF00515. D.A.R., G.N. and S.Ghimire were supported by the AMOS program within the Chemical Sciences, Geosciences, and Biosciences Division, DOE, BES, DOE. We thank R. Santra for discussions.

## Author information

Authors

### Contributions

M.F. and D.A.R. conceived and with S.B., C.K., S.Guillet and J.B.H. designed the experiment. S.H., G.A.C., J.P., P.H., C.K., S.Guillet, S.B., G.J.W. and M.M. designed and fabricated the components of the experiment. M.F., M.T., J.C., S.Ghimire, S.S., M.K., M.J., T.H., C.B., G.N., Y.F., S.H., S.M., J.B.H. and D.A.R. carried out the experiment. S.B., G.J.W., M.M. and M.M.S. operated the coherent X-ray imaging instrument. M.F., M.T. and J.C. analysed the data. M.F. and D.A.R. interpreted the results with input from P.H.B., and M.F. and D.A.R. wrote the manuscript with input from all other authors.

### Corresponding author

Correspondence to Matthias Fuchs.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 1623 kb)

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Fuchs, M., Trigo, M., Chen, J. et al. Anomalous nonlinear X-ray Compton scattering. Nature Phys 11, 964–970 (2015). https://doi.org/10.1038/nphys3452

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• DOI: https://doi.org/10.1038/nphys3452

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