In recent years, the field of light-matter interaction has made a further stride forward with the advent of superconducting qubits ultra-strongly coupled to open waveguides. In this setting, the qubit becomes simultaneously coupled to many different modes of the waveguide, thus turning into a highly intricate light-matter object [1].

In the main part of this talk, I will investigate theoretically the scattering of low-power coherent signals on such an ultra-strongly coupled qubit, a common experimental protocol performed routinely in laboratories. First, I will describe a new technique developed to tackle the dynamics of this complex many-body system that is based on the representation of the state vector in terms of a superposition of coherent states [2]. I will then present the main results obtained using this technique. Most remarkably, I will show that the qubit non-linearity, transferred to the waveguide through the ultra-strong light-matter interaction, is able to split photons from the incoming beam into several lower-energy photons [3]. Finally, by using the second-order correlation function in the scattered signal, I will present certain signatures of this phenomenon that can be expected in experiments.

[1] Martinez, J. P. et al. npj Quantum Information 5, 19 (2019).
[2] Gheeraert, N., Bera, S. & Florens, S. New J. Phys. 19 (2017)
[3] Gheeraert, N. et al. Phys. Rev. A 98, 043816 (2018)