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

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.

Impact of dephasing probes on incommensurate lattices

“…Although we use the AAH model as our underlying platform, our findings are easily extendable to other kinds of incommensurate models, including those that host mobility edges [61][62][63][64][65][66][67][68], which have also gained importance from an experimental perspective recently [51][52][53][54]. Our work can also be easily adaptable to other interesting setups such as the Frenkel-Kontorova model [69]. Our work is an important step forward in terms of engineering physical systems with various geometries that could host mixed dynamical phases.…”