Two emitters coupled to a bath with Kerr-like non-linearity: Exponential decay, fractional populations, and Rabi oscillations

TL;DR

This paper studies how two non-interacting emitters coupled to a nonlinear wave guide exhibit diverse radiation behaviors, including decay, fractional populations, and Rabi oscillations, due to the wave guide's non-trivial mode structure and bound states.

Contribution

It introduces a theoretical framework for analyzing two emitters coupled to a Kerr-like nonlinear wave guide, revealing complex dynamics and effective interactions influenced by non-linearity and emitter separation.

Findings

Observation of exponential decay, fractional populations, and Rabi oscillations.

Dependence of dynamics on emitter detuning and separation.

Effective models elucidate physical mechanisms and guide experimental tests.

Abstract

We consider two non-interacting two-level emitters that are coupled weakly to a one-dimensional non-linear wave guide. Due to the Kerr-like non-linearity, the wave guide considered supports -- in addition to the scattering continuum -- a two-body bound state. As such, the wave guide models a bath with non-trivial mode structure. Solving the time-dependent Schr\"odinger equation, the radiation dynamics of the two emitters, initially prepared in their excited states, is presented. Changing the emitter frequency such that the two-emitter energy is in resonance with one of the two-body bound states, radiation dynamics ranging from exponential decay to fractional populations to Rabi oscillations is observed. Along with the detuning, the dependence on the separation of the two emitters is investigated. Approximate reduced Hilbert space formulations, which result in effective emitter-separation and momentum dependent interactions, elucidate the underlying physical mechanisms and provide an avenue to showcase the features that would be absent if the one-dimensional wave guide did not contain a non-linearity. Our theoretical findings apply to a number of experimental platforms and the predictions can be tested with state-of-the-art technology. In addition, the weak-coupling Schr\"odinger equation based results provide critical guidance for the development of master equation approaches.