Injection and nucleation of topological defects in the quench dynamics of the Frenkel-Kontorova model

TL;DR

This paper explores how quench dynamics in the Frenkel-Kontorova model can be used to controllably inject topological defects, enabling the creation of superposition states and advancing experimental control in quantum simulators.

Contribution

It demonstrates a method to inject topological defects via quench dynamics in a Frenkel-Kontorova chain, with implications for quantum state engineering.

Findings

Quench from commensurate to incommensurate phase injects defects periodically.

Defects can be used to generate superposition states of lattice structures.

Provides experimental perspectives for defect control in trapped ion systems.

Abstract

Topological defects have strong impact on both elastic and inelastic properties of materials. In this article, we investigate the possibility to controllably inject topological defects in quantum simulators of solid state lattice structures. We investigate the quench dynamics of a Frenkel-Kontorova chain, which is used to model discommensurations of particles in cold atoms and trapped ionic crystals. The interplay between an external periodic potential and the inter-particle interaction makes lattice discommensurations, the topological defects of the model, energetically favorable and can tune a commensurate-incommensurate structural transition. Our key finding is that a quench from the commensurate to incommensurate phase causes a controllable injection of topological defects at periodic time intervals. We employ this mechanism to generate quantum states which are a superposition of lattice structures with and without topological defects. We conclude by presenting concrete perspectives for the observation and control of topological defects in trapped ion experiments.