  Strong and ultra-strong light-matter coupling are remarkable phenomena of
quantum electrodynamics occurring when the interaction between a matter
excitation and the electromagnetic field cannot be described by usual
perturbation theory. This is generally achieved by coupling an excitation with
large oscillator strength to the confined electromagnetic mode of an optical
microcavity. In this work we demonstrate that strong/ultra-strong coupling can
also take place in the absence of optical confinement. We have studied the
non-perturbative spontaneous emission of collective excitations in a dense
two-dimensional electron gas that superradiantly decays into free space. By
using a quantum model based on the input-output formalism, we have derived the
linear optical properties of the coupled system and demonstrated that its
eigenstates are mixed light-matter particles, like in any system displaying
strong or ultra-strong light-matter interaction. Moreover, we have shown that
in the ultra-strong coupling regime, i.e. when the radiative broadening is
comparable to the matter excitation energy, the commonly used rotating-wave and
Markov approximations yield unphysical results. Finally, the input-output
formalism has allowed us to prove that Kirchhoff's law, describing thermal
emission properties, applies to our system in all the light-matter coupling
regimes considered in this work.
