Nonperturbative and non-Markovian F\"{o}rster-interaction in waveguiding systems

An exact solution to the interaction between two emitters mediated by F\"{o}rster resonance energy transfer is presented. The system is comprised of a one-dimensional optical waveguide with two embedded two-level systems and is analyzed using a recently developed quantum-field theoretical approach. This exactly solvable model features several competing mechanisms that lead to a rich physical behavior such as, for instance, the possibility to change from an attractive to a repulsive interaction. Our nonperturbative analysis allows on very general grounds to describe the interaction as a truly non-Markovian phenomenon mediated by the atom-photon bound states of the system. These results are of direct relevance for energy or information transfer processes as well as for atom trapping more complex systems.