Electromagnetically induced transparency in many-emitter waveguide quantum electrodynamics: linear versus nonlinear waveguide dispersions

We study single-photon induced electromagnetically induced transparency (EIT) in many-emitter waveguide quantum electrodynamics (wQED) with linear and nonlinear waveguide dispersion relations. In the single-emitter problem, in addition to the robustness of the EIT spectral features in the over-coupled regime of wQED, we find that the nonlinear dispersion results in the appearance of a side peak for frequencies smaller than the resonant EIT frequency which turns into a pronounced plateau as the nonlinearity is enhanced. Consequently, for many-emitter scenarios, our results indicate the formation of band structure which for higher values of nonlinearity leads to narrow band gaps as compared to the corresponding linear dispersion case. Long-distance quantum networking aided with quantum memories can serve as one of the targeted applications of this work.