Nonperturbative decay dynamics in metamaterial waveguides

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