Strong coupling of virtual negative states in the Kapitza-Dirac effect

TL;DR

This paper demonstrates that negative states significantly influence the quantum diffraction process in the two-photon Kapitza-Dirac effect, linking relativistic quantum theory with observable phenomena.

Contribution

It reveals the dominant role of negative states in the Kapitza-Dirac effect through combined analytical and numerical analysis, extending understanding of relativistic quantum interactions.

Findings

Negative states significantly contribute to diffraction amplitude.

Negative state coupling remains dominant at low laser field amplitudes.

Virtual electron-positron pairs are related to negative state interactions.

Abstract

Negative states are an intrinsic property of relativistic quantum theory and related to anti-particles in the context of the Dirac sea concept. We show that negative states can dominantly contribute to the diffraction amplitude in the quantum dynamics of the two-photon Kapitza-Dirac effect. We draw our conclusion by investigating solutions from time-dependent perturbation theory, where the perturbative solutions are in match with numeric solutions of the relativistic quantum system and also with the numeric and analytic solutions from the relativistic equations of motion of a classical point-like electron in an external standing wave light field. While our numeric solutions assume a strong laser field, the analytic solutions indicate that negative state coupling remains dominant for arbitrary low field amplitudes, where in the single-photon case (Compton scattering) negative state coupling can be mathematically associated with the interaction of a virtual electron-positron pair in the context of a quantized theory in old-fashioned perturbation theory.