Interference in nonlinear Compton scattering

We study the interference between Compton and nonlinear Compton scattering from bound electrons using a two-color field in the x-ray regime theoretically. The underlying phase shifts are analyzed using a perturbative approach in the incoming classical field. A non-perturbative approach in the classical field is used to benchmark the perturbative approach. The interference is examined for different combinations of linear polarization of the two fields when the Compton and the nonlinear Compton scattered waves have the same wave vector and polarization. The interference is found to occur only for two cases. When it does occur, there exists an intrinsic phase difference between the Compton and nonlinear Compton scattered wave function of either 0 or π depending on the scattering angle.