One-dimensional photonic wire as a single-photon source: Implications of cavity QED to a phonon bath of reduced dimensionality

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 (1D) 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.