  Josephson circuits provide a realistic physical setup where the light-matter
fine structure constant can become of order one, allowing to reach a regime
dominated by non-perturbative effects beyond standard quantum optics. Simple
processes, such as spontaneous emission, thus acquire a many-body character,
that can be tackled using a new description of the time-dependent state vector
in terms of quantum-superposed coherent states. We find that spontaneous atomic
decay at ultrastrong coupling leads to the emission of spectrally broad
Schr\"odinger cats rather than of monochromatic single photons. These cats
states remain partially entangled with the emitter at intermediate stages of
the dynamics, even after emission, due to a large separation in time scales
between fast energy relaxation and exponentially slow decoherence. Once
decoherence of the qubit is finally established, quantum information is
completely transfered to the state of the emitted cat.
