Topological soliton-polaritons in 1D systems of light and fermionic matter

TL;DR

This paper introduces a novel type of topological soliton-polariton in 1D light-fermion systems, which are intrinsically nonlinear, carry a $ extbf{Z}_2$ topological quantum number, and resemble SSH model solitons.

Contribution

It presents the theoretical concept of topological soliton-polaritons formed by fermions trapped in optical solitons with topological properties, linking quantum nonlinear optics and topological matter.

Findings

Identification of soliton-polaritons with topological quantum numbers

Connection to the SSH model for topological states

Proposal of a new quasi-particle in quantum optics

Abstract

Quantum nonlinear optics is a quickly growing field with large technological promise, at the same time involving complex and novel many-body phenomena. In the usual scenario, optical nonlinearities originate from the interactions between polaritons, which are hybrid quasi-particles mixing matter and light degrees of freedom. Here we introduce a type of polariton which is intrinsically nonlinear and emerges as the natural quasi-particle in presence quantum degenerate fermionic matter. It is a composite object made of a fermion trapped inside an optical soliton forming a topological defect in a spontaneously formed crystalline structure. Each of these soliton-polaritons carries a $\textbf{Z}_2$ topological quantum number, as they create a domain wall between two crystalline regions with opposite dimerization so that the fermion is trapped in an interphase state. These composite objects are formally equivalent to those appearing in the Su-Schrieffer-Heeger (SSH) model for electrons coupled to lattice phonons.