  Here we present the theoretical foundation of the strong coupling phenomenon
between quantum emitters and propagating surface plasmons observed in
two-dimensional metal surfaces. For that purpose, we develop an ab-initio
quantum framework that accounts for the coherent coupling be- tween emitters
and surface plasmons and incorporates the presence of dissipation and
dephasing. For both a single emitter and a disordered ensemble of emitters, our
formalism is able to reveal the key physical mechanisms that explain the
reported phenomenology and also to determine the physical parameters that
optimize the strong coupling.
