Solving the scattering of N photons on a two-level atom without computation

TL;DR

This paper introduces a new analytical method for solving light scattering by a two-level atom in a waveguide, avoiding complex computations by using Feynman diagrams and linear approximations.

Contribution

The paper presents a novel, non-computational approach to model photon-atom scattering, leveraging Feynman diagrams and atomic response to simplify the analysis.

Findings

Derives scattering outcomes using simple integrals over incoming wavepackets.

Captures atomic excitation dynamics during scattering events.

Provides a general framework applicable to various scattering scenarios.

Abstract

We propose a novel approach for solving the scattering of light onto a two-level atom coupled to a one-dimensional waveguide. We first express the physical quantity of interest in terms of Feynman diagrams and treat the atom as a non-saturable linear beamsplitter. By using the atomic response to our advantage, a relevant substitution is then made that captures the nonlinearity of the atom, and the final result is obtained in terms of simple integrals over the initial incoming wavepackets. The procedure is not limited to post-scattering quantities and allows for instance to derive the atomic excitation during the scattering event.