Quantum optical properties of a dipole emitter coupled to an ɛ-near-zero nanoscale waveguide

We study quantum optical properties of a dipole emitter coupled to a rectangular nanoscale waveguide with dielectric core and silver cladding. We investigate enhanced spontaneous emission and the photonic Lamb shift for emitters whose resonant frequencies are near the waveguide frequency cutoff where the waveguide behaves as an ɛ-near-zero metamaterial. Via a dyadic Green's function-based field quantization scheme, we calculate the photonic Lamb shift as well as the spontaneous emission enhancement and spectrum. Using realistic parameters for typical quantum emitters, we suggest experimentally realizable schemes to observe relatively large photonic Lamb shifts in waveguides.