  While the semiconductor quantum dot placed in a solid-state material allows
for deterministic emission of single photons, the photon indistinguishability
is strongly influenced by the intrinsic coupling to lattice vibrations,
phonons, of the solid-state environment. This work investigates the
phonon-induced decoherence for a quantum dot placed in the one-dimensional
system of a homogeneous cylindrical nanowire. Such a structure supports
multiple longitudinal phonon branches, and we consider both a linear and a
quadratic coupling of the emitter to these modes. Under a polaron approach, we
initially derive an analytical expression for the 1D pure dephasing rate, which
leads to a reduced pure dephasing rate compared with bulk. By implementing
these results into a full cavity quantum electrodynamic model, we demonstrate
that multimode coupling is necessary to correctly predict the
indistinguishability in a 1D system, which may otherwise be significantly
underestimated.
