Ultrastrong Coupling Few-Photon Scattering Theory

We study the scattering of individual photons by a two-level system ultrastrongly coupled to a waveguide. The scattering is elastic for a broad range of couplings and can be described with an effective U(1)-symmetric Hamiltonian. This simple model allows the prediction of scattering resonance line shapes, validated up to alpha = 0.3, and close to the Toulouse point alpha = 1/2, where inelastic scattering becomes relevant. Our predictions model experiments with superconducting circuits [P. Forn-Diaz et al.,Nat.Phys.13, 39 (2017)] and can be extended to study multiphoton scattering.