Probing the topological properties of the Jackiw-Rebbi model with light

TL;DR

This paper demonstrates how the topological properties of the Jackiw-Rebbi model can be simulated using a driven slow-light optical setup, allowing exploration of zero-energy modes and charge fractionalization with photons.

Contribution

The study introduces a novel optical implementation of the Jackiw-Rebbi model using slow-light systems, enabling experimental probing of topological zero-modes and their stability.

Findings

Zero-energy mode can be realized in the optical setup.

Transmission spectrum reveals the presence of the topological zero-mode.

Robustness of the topological features against experimental errors is analyzed.

Abstract

The Jackiw-Rebbi model describes a one-dimensional Dirac particle coupled to a soliton field and can be equivalently thought of as the model describing a Dirac particle under a Lorentz scalar potential. Neglecting the dynamics of the soliton field, a kink in the background soliton profile yields a topologically protected zero-energy mode for the particle, which in turn leads to charge fractionalization. We show here that the model can be realized in a driven slow-light setup, where photons mimic the Dirac particles and the soliton field can be implemented-and tuned-by adjusting optical parameters such as the atom-photon detuning. Furthermore, we discuss how the existence of the zero-mode, and its topological stability, can be probed naturally by analyzing the transmission spectrum. We conclude by doing an analysis of the robustness of our approach against possible experimental errors in engineering the Jackiw-Rebbi Hamiltonian in this optical set up.