Fully quantum-mechanical analytic results for single-photon transport in a single-mode waveguide coupled to a whispering-gallery resonator interacting with a two-level atom

TL;DR

This paper provides exact quantum-mechanical solutions for single-photon transport in a waveguide coupled to a whispering-gallery resonator interacting with a two-level atom, including effects of backscattering and dissipation.

Contribution

It offers a comprehensive analytical framework for understanding single-photon transport in complex waveguide-resonator-atom systems, including generalized critical coupling conditions.

Findings

Exact expressions for transmission and reflection amplitudes.

Inclusion of backscattering and dissipation effects.

Validation of a generalized critical coupling condition.

Abstract

We analyze the single-photon transport in a single-mode waveguide coupled to a whispering-gallery-type resonator interacting with a two-level atom. The single-photon transport properties such as the transmission and reflection amplitudes, as well as the resonator and the atom responses, are solved exactly via a real-space approach. The treatment includes the inter-mode backscattering between the two degenerate whispering gallery modes of the resonator, and the dissipations of the resonator and the atom. We also show that a generalized critical coupling condition, that the single-photon transmission at the output of the waveguide goes to zero on resonance for a matched system, holds for the full coupled waveguide-ring resonator-atom system.