Nonresonant quantum dynamics of a relativistic electron in counterpropagating laser beams

Abstract: The quantum dynamics of an ultrarelativistic electron in strong counterpropagating laser beams is investigated. In contrast to the stimulated Compton scattering regime, we consider the case when in the electron rest frame the frequency of the counterpropagating wave greatly exceeds that of the copropagating one. Taking advantage of the corresponding approximation recently developed by the authors for treating the classical dynamics in this setup, we solve the Klein-Gordon and Dirac equations in the quasiclassical approximation in the Wentzel-Kramers-Brillouin (WKB) framework. The obtained wave function for the Dirac equation shows entanglement between the kinetic momentum and spin of the electron, while the spin-averaged momentum coincides with the classical counterpart as expected. The derived wave functions will enable the calculation of the probabilities of nonlinear QED processes in this counterpropagating fields configuration.