  Understanding large-scale interacting quantum matter requires dealing with
the huge number of quanta that are produced by scattering even a few particles
against a complex quantum object. Prominent examples are found from high energy
cosmic ray showers to the optical or electrical driving of degenerate Fermi
gases. We tackle this challenge in the context of many-body quantum optics, as
motivated by the recent developments of circuit quantum electrodynamics at
ultrastrong coupling. The issue of particle production is addressed
quantitatively with a simple yet powerful concept rooted in the quantum
superposition principle. This key idea is illustrated by the study of
multi-photon emission from a single two-level artificial atom coupled to a high
impedance waveguide. We find surprisingly that the off-resonant inelastic
emission lineshape is dominated by broadband particle production, due to the
large phase space associated with contributions that do not conserve the number
of excitations. Such frequency conversion processes produce striking signatures
in time correlation measurements, which can be tested experimentally in quantum
waveguides. These ideas open new directions for the simulation of a variety of
physical systems, from polaron dynamics in solids to complex superconducting
quantum architectures.
