  Cavity quantum electrodynamics advances the coherent control of a single
quantum emitter with a quantized radiation field mode, typically piecewise
engineered for the highest finesse and confinement in the cavity field. This
enables the possibility of strong coupling for chip-scale quantum processing,
but till now is limited to few research groups that can achieve the precision
and deterministic requirements for these polariton states. Here we observe for
the first time coherent polariton states of strong coupled single quantum dot
excitons in inherently disordered one-dimensional localized modes in slow-light
photonic crystals. Large vacuum Rabi splittings up to 311 {\mu}eV are observed,
one of the largest avoided crossings in the solid-state. Our tight-binding
models with quantum impurities detail these strong localized polaritons,
spanning different disorder strengths, complementary to model-extracted pure
dephasing and incoherent pumping rates. Such disorder-induced slow-light
polaritons provide a platform towards coherent control, collective
interactions, and quantum information processing.
