Scattering theory in the ultrastrong coupling regime

The ultrastrong coupling regime is the one which the light-matter interaction strength is comparable to the energy of the photons and atoms (or qubits) involved. A recent experiment using flux qubits\footnote{P. Forn-Díaz et al, Nature Physics (to appear)} has demonstrated this regime for superconducting circuits and propagating microwave photons, with coupling strengths that go well into the localization phase. In this talk I will present a theoretical framework that can be used to describe the scattering of photons by a two-level system using a combination of the polaron ansatz\footnote{G. Díaz-Camacho et al, Phys. Rev. A 93, 043843 (2016)} and S-matrix formalism\footnote{T. Shi, D.E. Chang, I. Cirac, Phys. Rev. A 92, 053834 (2015)}. This results in quantiative estimates of resonances and lineshapes and can be used to estimate the coupling strength of a dressed artificial atom interacting with a one-dimensional bosonic field. This theoretical approach allows also exploring the potential of the ultrastrong coupling regime for engineering nonlinearities, photon-photon interactions and photon-mediated spin-models.