Quantum phase transition and interference trapping of populations in a coupled-resonator waveguide

Abstract

We study the energy structure and dynamics of a V-type three-level emitter embedded in a one-dimensional waveguide with model dispersion. Due to the presence of two different couplings between the upper levels and the waveguide modes, we find that the bound states in this system are quite different from the case of a two-level emitter. The energy structure is dependent on the relative position of the emitter's transition frequencies from the band with finite width. We obtain the phase diagrams through numerical analysis. The dynamics of spontaneous emission of the system is calculated exactly in the general case by means of the Green's function approach. The emitted photon is characterized by two components: a localized part and a traveling part, and the average frequency of the traveling part is different from that for resonant scattering. Through the quantum interference between the emitter's two transitions, it is found that the total excitation number of the localized photon and emitter can be greatly enhanced in some case in the spontaneous-emission process.