Nonperturbative decay dynamics in metamaterial waveguides

In this work we investigate the nonperturbative decay dynamics of a quantum emitter coupled to composite right/left handed transmission line (CRLH-TL). Our theory captures contributions from different spectral features waveguide, providing an accurate prediction beyond weak coupling regime, and illustrating multiple possibilities offered by nontrivial dispersion metamaterial waveguides. We show that waveguide is characterized band-gap with two asymmetric edges: (i) mu-near-zero (MNZ) band edge, where spontaneous emission inhibited unstable pole smoothly transformed into bound state, (ii) epsilon-near-zero (ENZ) rate diverges real (bound state) poles coexist. both cases, branch cut singularities contribute fractional whose nature depend on properties band-edges.