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Nonlinear Compton scattering is an inelastic scattering process where aphoton is emitted due to the interaction between an electron and an intenselaser field. With the development of X-ray free-electron lasers, the intensityof X-ray laser is greatly enhanced, and the signal from X-ray nonlinear Comptonscattering is no longer weak. Although the nonlinear Compton scattering by aninitially free electron has been thoroughly investigated, the mechanis ofnonrelativistic nonlinear Compton scattering of X-ray photons by boundelectrons is unclear yet. Here, we present a frequency-domain formulation basedon the nonperturbative quantum electrodynamic to study nonlinear Comptonscattering of two photons off a bound electron inside an atom in a strong X-raylaser field. In contrast to previous theoretical works, our results clearlyreveal the existence of anomalous redshift phenomenon observed experimentallyby Fuchs et al. (Nat. Phys. 11, 964 (2015)) and suggest its origin as thebinding energy of the electron as well as the momentum transfer from incidentphotons to the electron during the scattering process. Our work builds a bridgebetween intense-laser atomic physics and Compton scattering process that can beused to study atomic structure and dynamics at high laser intensities.

Explanation of the anomalous redshift on nonlinear X-ray Compton scattering spectrum by a bound electron