Efficient entanglement between two long-distance quantum emitters mediated by dark-gap-plasmon waveguides

We theoretically investigate the entanglement between two well-separated quantum emitters (QEs) mediated by dark-gap-plasmon waveguides. Both the plasmon-QE coupling strength and the energy transfer efficiency between QEs are crucial for entanglement based on analytical results. To overcome the low energy transfer efficiency brought by common plasmonic waveguides, we construct a simple dark-gap-plasmon waveguide. Such a structure consists of two parallel silver nanowires, where dark plasmon modes are formed in the gap between the two nanowires. The leaky (or radiative) feature of propagating plasmons is highly suppressed, which results in the quality factors of the dark plasmon modes reaching the material limit. Thus, the energy transfer efficiency can reach more than 94% with a distance even over ten working wavelengths ($>10\mu m$). Meanwhile, by introducing a tip dimer structure in the nanowire gap, the plasmon-QE coupling can reach a strong coupling regime with realistic parameters. The influences from the geometric parameters of the system are also considered. The energy transfer efficiency is robust to the geometric variations due to the dark feature of the plasmon responses.