We study the scattering of photons by a two-level system ultrastrongly coupled to a one-dimensional waveguide. Using a combination of the polaron transformation with scattering theory we can compute the one-photon scattering properties of the qubit for a broad range of coupling strengths, estimating resonance frequencies, lineshapes and linewidths. We validate numerically and analytically the accuracy of this technique up to α=0.3, close to the Toulouse point α=1/2, where inelastic scattering becomes relevant. These methods model recent experiments with superconducting circuits [P. Forn-D{\'\i}az et al., Nat. Phys. (2016)].
@article{arxiv.1701.04709,
title = {Ultrastrong coupling few-photon scattering theory},
author = {Tao Shi and Yue Chang and Juan Jose Garcia-Ripoll},
journal= {arXiv preprint arXiv:1701.04709},
year = {2018}
}