  In this work we develop a semi-analytical variational ansatz to study the
properties of few photon excitations interacting with a collection of quantum
emitters in regimes that go beyond the rotating wave approximation. This method
can be used to approximate both the static and dynamical properties of a
superconducting qubit in an open transmission line, including the spontaneous
emission spectrum and the resonances in scattering experiments. The
approximations are quantitatively accurate for rather strong couplings, as
shown by a direct comparison to Matrix-Product-State numerical methods, and
provide also a good qualitative description for stronger couplings well beyond
the Markovian regime.
