Single Photon Two-Level Atom Interactions in 1-D Dielectric Waveguide: Quantum Mechanical Formalism and Applications

TL;DR

This paper develops a quantum mechanical model for a two-level atom interacting with light in a 1-D dielectric waveguide, revealing novel transport properties and applications in quantum optics devices.

Contribution

It introduces a macroscopic Hamiltonian formalism that incorporates media effects and derives non-classical Fresnel laws, advancing the understanding of atom-waveguide interactions.

Findings

Demonstrates non-classical Fresnel Law derivation

Analyzes high-Q bandreject filter properties

Studies emission variations in modified interferometers

Abstract

In this paper, we propose an effective model including a macroscopic Hamiltonian to describe the interactions between a two-level atom and scattered light in a 1-D dielectric waveguide. The proposed formalism allows us to incorporate the effect of changing optical media inside the continuum while demonstrating a non-classical derivation of Fresnel Law. We obtain the transport characteristics of the two-level system, explore its high-Q bandreject filter property and discuss the implications of radiative and non-radiative dissipation. In addition, we apply our formalism to a modified Fabry-P\'{e}rot interferometer and show the variation in its spontaneous emission characteristics with changing interferometer length. Finally, we conclude with further remarks on the link between the waveguide and cavity quantum electrodynamics.