  Heisenberg's uncertainty principle implies that the quantum vacuum is not
empty but fluctuates. These fluctuations can be converted into radiation
through nonadiabatic changes in the Hamiltonian. Here, we discuss how to
control this vacuum radiation, engineering a single-photon emitter out of a
two-level system (2LS) ultrastrongly coupled to a finite-band waveguide in a
vacuum state. More precisely, we show the 2LS nonlinearity shapes the vacuum
radiation into a nonGaussian superposition of even and odd cat states. When the
2LS bare frequency lays within the band gaps, this emission can be well
approximated by individual photons. This picture is confirmed by a
characterization of the ground and bound states, and a study of the dynamics
with matrix product states and polaron Hamiltonian methods.
