  Decay of a particle into more particles is a ubiquitous phenomenon to
interacting quantum systems, taking place in colliders, nuclear reactors, or
solids. In a non-linear medium, even a single photon would decay by
down-converting (splitting) into lower frequency photons with the same total
energy, at a rate given by Fermi's Golden Rule. However, the energy
conservation condition cannot be matched precisely if the medium is finite and
only supports quantized modes. In this case, the photon's fate becomes the
long-standing question of many-body localization (MBL), originally formulated
as a gedanken experiment for the lifetime of a single Fermi-liquid
quasiparticle confined to a quantum dot. Here we implement such an experiment
using a superconducting multi-mode cavity, the non-linearity of which was
tailored to strongly violate the photon number conservation. The resulting
interaction attempts to convert a single photon excitation into a shower of
low-energy photons, but fails due to the MBL mechanism, which manifests as a
striking spectral fine structure of multi-particle resonances at the cavity's
standing wave mode frequencies. Each resonance was identified as a many-body
state of radiation composed of photons from a broad frequency range, and not
obeying the Fermi's Golden Rule theory. Our result introduces a new platform to
explore fundamentals of MBL without having to control many atoms or qubits.
