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

小型激光冷却囚禁离子阵列的实验已经证明了在实现大规模量子信息处理的最终目标方面取得了令人印象深刻的技术成就。这些成就的核心是离子阱、激光和其他技术，这些技术可以在单原子水平上对实验参数进行精确控制。利用这些技术，我们的目标是使用离子之间的相互作用-来自它们的库仑排斥以及陷阱和其他应用的电磁场-来研究多体物理学，让人想起凝聚态中熟悉的模型。 我们的研究集中在激光冷却和囚禁镱离子阵列中的线性-锯齿形结构相变。这种转变的二阶性质，以及它可以在实验装置内控制的相对简单性，使得一个迷人的测试平台可以在经典和量子制度，非线性动力学和非平衡统计力学中研究介观相变。我们计划测试的Kibble-Zurek机制拓扑缺陷的形成，提高了之前的实验，我们的团队和其他人的淬火跨越线性锯齿过渡。我们还计划在新的方向出击，研究结构转变附近的离子晶体作为低维系统中热传输的可调模型，并研究对应于几个量子或更少热能的超低温下的转变。在后一种情况下，我们的目标是利用双阱势，发展附近的过渡，以控制离子晶体的两个锯齿形结构之间的隧穿，实现可调介观系统让人想起氨分子。 无论是量子力学的基础测试还是模型材料中动力学的研究，该计划都旨在推动被困离子实验控制的极限。在这样做的过程中，这项资助所实现的技术将在相关的捕获离子量子技术领域产生影响，事实上，无论在哪里，量子力学操纵信息正在被调查，如量子信息处理，纳米技术和材料研究领域。

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.