  Coherent photon-emitter interfaces offer a way to mediate efficient nonlinear
photon-photon interactions, much needed for quantum information processing.
Here we experimentally study the case of a two-level emitter, a quantum dot,
coupled to a single optical mode in a nanophotonic waveguide. We carry out
few-photon transport experiments and record the statistics of the light to
reconstruct the scattering matrix elements of 1- and 2-photon components. This
provides direct insight to the complex nonlinear photon interaction that
contains rich many-body physics.
