Real-time collisions of fractional charges in a trapped-ion Jackiw-Rebbi field theory

TL;DR

This paper presents a trapped-ion quantum simulator for the Jackiw-Rebbi model, exploring how quantum fluctuations and back-reaction influence fractional charge excitations and their dynamics in a controllable experimental setup.

Contribution

It introduces a novel trapped-ion implementation of the Jackiw-Rebbi model, analyzing the effects of back-reaction and quantum fluctuations on fractionalized fermions.

Findings

Back-reaction can localize topological kinks.

Quantum fluctuations cause spreading and scattering of kinks.

Predicted observable signatures in current trapped-ion experiments.

Abstract

We propose and analyze a trapped-ion quantum simulator of the Jackiw-Rebbi model, a paradigmatic quantum field theory in (1+1) dimensions where solitonic excitations of a scalar field can bind fermionic zero modes leading to fractionally-charged excitations. In our approach, the scalar field is a coarse-grained description of the planar zigzag ion displacements in the vicinity of a structural phase transition. The internal electronic states of the ions encode spins with interactions mediated by the transverse phonons and in-plane spin-phonon couplings with a zigzag pattern, which together correspond to a Yukawa-coupled Dirac field. Instead of assuming a fixed soliton background, we study the effect of back-reaction and quantum fluctuations on the coupled dynamics of the full fermion-boson system. We start by applying a Born-Oppenheimer approximation to obtain an effective Peierls-Nabarro potential for the topological kink, unveiling how the fermionic back-reaction can lead to localization of the kink. Beyond this limit, a truncated Wigner approximation combined with fermionic Gaussian states captures the quantum spreading and localization of a kink and kink-antikink scattering. Our results reveal how back-reaction and quantum fluctuations modify the stability and real-time evolution of fractionalized fermions, predicting experimentally accessible signatures in current trapped-ion architectures.