Bright and dark solitons in the systems with strong light-matter coupling: exact solutions and numerical simulations

TL;DR

This paper provides exact analytical solutions and numerical analysis of bright and dark solitons in a strongly coupled light-matter system, revealing diverse stable and unstable soliton behaviors and their relation to the system's dispersion properties.

Contribution

It introduces a unified analytical framework for coexisting bright and dark solitons in a two-component model with strong light-matter coupling, linking solutions to the polariton dispersion.

Findings

Multiple types of coexisting solitons identified

Bright solitons exhibit oscillatory-instability thresholds

Dark-gray and gray-gray solitons are stable over wide parameters

Abstract

We theoretically study bright and dark solitons in an experimentally relevant hybrid system characterized by strong light-matter coupling. We find that the corresponding two-component model supports a variety of coexisting moving solitons including bright solitons on zero and nonzero background, dark-gray and gray-gray dark solitons. The solutions are found in the analytical form by reducing the two-component problem to a single stationary equation with cubic-quintic nonlinearity. All found solutions coexist under the same set of the model parameters, but, in a properly defined linear limit, approach different branches of the polariton dispersion relation for linear waves. Bright solitons with zero background feature an oscillatory-instability threshold which can be associated with a resonance between the edges of the continuous spectrum branches. `Half-topological' dark-gray and nontopological gray-gray solitons are stable in wide parametric ranges below the modulational instability threshold, while bright solitons on the constant-amplitude pedestal are unstable.