  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.
