  We study spontaneous photon decay into multiple photons triggered by strong
non-linearities in a superconducting quantum simulator of the boundary
sine-Gordon impurity model. Previously, spectroscopic signatures of
photon-conversion were reported and evidenced as resonances in the many-body
spectrum of these systems. Here, we report on the observation of multi-mode
fluorescence of a small Josephson junction embedded in a high impedance
superconducting transmission line. Measurement of the down-converted photons is
achieved using state-of-the-art broadband parametric amplifiers. Photon triplet
emission is explicitly demonstrated at a given frequency as the counterpart of
inelastic photon decay at three-times the emission frequency. These results
open exciting prospects for the burgeoning field of many-body quantum optics
and offer a direct signature of the ultra-strong light-matter coupling.
