Using a Trapped-Ion Simulator to Explore Mesoscopic Systems with Individual Atom Resolution

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Experiments with small arrays of laser-cooled trapped ions have demonstrated an impressive number of technical achievements towards the ultimate goal of large scale quantum information processing. At the heart of these achievements are ion-trap, laser, and other technologies that deliver exquisite control over experimental parameters at the level of single atoms. Taking advantage of these technologies, we aim to use the interactions between ions - derived from their Coulomb repulsion together with the trap and other applied electromagnetic fields - to investigate many-body physics with a flavor reminiscent of familiar models in condensed matter. Our investigations focus on the linear-zigzag structural phase transition in laser-cooled and trapped arrays of Ytterbium ions. The second-order nature of this transition, and the relative simplicity with which it can be controlled within an experimental setup, make for a fascinating testbed to investigate mesoscopic phase transitions in both the classical and quantum regimes, nonlinear dynamics, and non-equilibrium statistical mechanics. We plan a test of the Kibble-Zurek mechanism for topological defect formation that improves upon prior experiments by our group and others for quenches across the linear-zigzag transition. We also plan to strike out in new directions, to investigate an ion crystal near the structural transition as a tunable model of heat transport in low-dimensional systems, and to investigate the transition at ultralow temperatures corresponding to a few quanta or less of thermal energy. In the latter case, our goal is to take advantage of the double-well potential that develops near the transition to control tunneling between the two zigzag structures of an ion crystal, realizing a tunable mesoscopic system reminiscent of the ammonia molecule. Be it for fundamental tests of quantum mechanics or for the investigation of dynamics in model materials, this program aims to push the limits of experimental control of trapped ions. In doing so, the techniques enabled by this grant will have an impact in the associated area of trapped-ion quantum technology, and indeed wherever quantum mechanical manipulation of information is being investigated, such as the areas of quantum information processing, nanotechnology, and materials research.