Scattering of slow-light gap solitons with charges in a two-level medium

TL;DR

This paper investigates how slow-light gap solitons in a two-level medium interact with charges, leading to scattering, trapping, or reflection, modeled via a nonlinear Schrödinger equation with an external potential.

Contribution

It introduces a model describing the scattering of slow-light gap solitons with charges in a two-level medium, highlighting the nonlinear coupling effects at resonance.

Findings

Slow-light gap solitons can be trapped or reflected by charges.

Scattering is governed by a nonlinear Schrödinger model with an external potential.

The quantum population density variation causes nonlinear effects at resonance.

Abstract

The Maxwell-Bloch system describes a quantum two-level medium interacting with a classical electromagnetic field by mediation of the the population density. This population density variation is a purely quantum effect which is actually at the very origin of nonlinearity. The resulting nonlinear coupling possesses particularly interesting consequences at the resonance (when the frequency of the excitation is close to the transition frequency of the two-level medium) as e.g. slow-light gap solitons that result from the nonlinear instability of the evanescent wave at the boundary. As nonlinearity couples the different polarizations of the electromagnetic field, the slow-light gap soliton is shown to experience effective scattering whith charges in the medium, allowing it for instance to be trapped or reflected. This scattering process is understood qualitatively as being governed by a nonlinear Schroedinger model in an external potential related to the charges (the electrostatic permanent background component of the field).