  Harnessing the interaction between light and matter at the quantum level has
been a central theme in atomic physics and quantum optics, with applications
from quantum computation to quantum metrology. Combining complex interactions
with photonic synthetic materials provides an opportunity to investigate novel
quantum phases and phenomena, establishing interesting connections to condensed
matter physics. Here we explore many-body phenomena with a single artificial
atom coupled to the many discrete modes of a photonic crystal. This experiment
reaches the ultrastrong light-matter coupling regime using the circuit quantum
electrodynamics paradigm, by galvanically coupling a highly nonlinear fluxonium
qubit to a tight-binding lattice of microwave resonators. In this regime, the
transport of a single photon becomes a many-body problem, owing to the strong
participation of multi-photon bound states arising from interactions that break
particle number conservation. Exploiting the effective photon-photon
interactions mediated by the qubit, the transport of multiple photons leads to
complex multimode dynamics that can be employed for generating a continuous
reservoir of strongly-correlated photons, an important resource for quantum
networks. This work opens exciting prospects for exploring nonlinear quantum
optics at the single-photon level and stabilizing entangled many-body phases of
light.
