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

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.