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

Understand

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.