  Usually, the liner waveguides with single quantum emitters are utilized as
routers to construct the quantum network in quantum information processings.
Here, we investigate the influence of the nonlinear dispersion on quantum
routing of single surface plasmons, between two metal nanowires with a pair of
quantum dots. By using a full quantum theory in real space, we obtain the
routing probabilities of a single surface plasmon into the four outports of two
plasmonic waveguides scattered by a pair of quantum dots. It is shown that, by
properly designing the inter-dot distance and the dot-plasmon couplings, the
routing capability of the surface plasmons between the plasmonic waveguide
channels can be significantly higher than the relevant network formed by the
single-emitter waveguides with the linear dispersions. Interestingly, the
present quadratic dispersions in the waveguides deliver the manifest Fano-like
resonances of the surface-plasmon transport. Therefore, the proposed double-dot
configuration could be utilized as a robust quantum router for controlling the
surface-plasmon routing in the plasmonic waveguides and a plasmonic Fano-like
resonance controller.
