  Waveguide quantum electrodynamics studies photon-mediated interactions of
quantum emitters in a one-dimensional radiation channel. Although signatures of
such interactions have been observed previously in a variety of physical
systems, observation of coherent cooperative dynamics has been obscured by
radiative decay of atoms into the waveguide. Employing transmon qubits as
artificial atoms coupled to a microwave coplanar waveguide, here we observe
dynamical oscillations in an open system where a designated probe qubit
interacts with an entangled dark state of an array of qubits which effectively
traps radiation as an atomic cavity. The qubit-cavity system is shown to
achieve a large cooperativity of $\mathcal{C}=172$ due to collective
enhancement of photon-mediated interactions, entering the strong coupling
regime. The quantum coherence of the dark state cavity is also explored through
its nonlinear response at the single-excitation level. With realistic
refinements, this system is suitable for studying the many-body dynamics of
large ($N>10$) quantum spin chains, synthesizing highly non-classical radiation
fields on demand, and implementing universal quantum logic operations with high
fidelity on information encoded within decoherence-free subspaces.
