Spontaneous nucleation of topological defects in trapped Yb^+ ion-crystals

Sara Ejtemaee, P. C. Haljan

Heather L. Partner, Ramil Nigmatullin, T. Burgermeister +7 more

Sara Ejtemaee, P. C. Haljan

The spontaneous nucleation and dynamics of topological kink defects have been studied in trapped arrays of 41--43 Yb ions. The number of kinks formed as a function of quench rate across the linear-zigzag transition is measured in the underdamped regime of the inhomogeneous Kibble-Zurek theory. The experimental results agree well with molecular dynamics simulations, which show how losses mask the intrinsic nucleation rate. Simulations indicate that doubling the ion number and optimization of laser cooling can help reduce the effect of losses. A range of kink dynamics is observed including configural change, motion and lifetime, and behavioral sensitivity to ion number.

Philipp T. Dumitrescu, Justin Bohnet, John Gaebler +6 more

Oksana Chelpanova, Shane P. Kelly, Giovanna Morigi +2 more

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.

Gabriele De Chiara, Campo, Adolfo del, Giovanna Morigi +2 more

Structural defects in ion crystals can be formed during a linear quench of the transverse trapping frequency across the mechanical instability from a linear chain to a zigzag structure. The density of defects after the sweep can be conveniently described by the Kibble–Zurek mechanism (KZM). In particular, the number of kinks in the zigzag ordering can be derived from a time-dependent Ginzburg–Landau equation for the order parameter, here the zigzag transverse size, under the assumption that the ions are continuously laser cooled. In a linear Paul trap, the transition becomes inhomogeneous, since the charge density is larger in the center and more rarefied at the edges. During the linear quench, the mechanical instability is first crossed in the center of the chain, and a front, at which the mechanical instability is crossed during the quench, is identified that propagates along the chain from the center to the edges. If the velocity of this front is smaller than the sound velocity, the dynamics become adiabatic even in the thermodynamic limit and no defect is produced. Otherwise, the nucleation of kinks is reduced with respect to the case in which the charges are homogeneously distributed, leading to a new scaling of the density of kinks with the quenching rate. The analytical predictions are verified numerically by integrating the Langevin equations of motion of the ions, in the presence of a time-dependent transverse confinement. We argue that the non-equilibrium dynamics of an ion chain in a Paul trap constitutes an ideal scenario to test the inhomogeneous extension of the KZM, which lacks experimental evidence to date.