  Coherent interactions between quantum emitters in tailored photonic
structures is a fundamental building block for future quantum technologies, but
remains challenging to observe in complex solid-state environments, where the
role of decoherence must be considered. Here, we investigate the optical
interaction between two quantum emitters mediated by one-dimensional waveguides
in a realistic solid-state environment, focusing on the creation, population
and detection of a sub-radiant state, in the presence of dephasing. We show
that as dephasing increases, the signatures of sub-radiance quickly vanish in
intensity measurements yet remain pronounced in photon correlation
measurements, particularly when the two emitters are pumped separately so as to
populate the sub-radiant state efficiently. The applied Green's tensor approach
is used to model a photonic crystal waveguide, including the dependence on the
spatial position of the integrated emitter. The work lays out a route to the
experimental realization of sub-radiant states in nanophotonic waveguides
containing solid-state emitters.
