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

用激光冷却的囚禁离子的小阵列进行的实验证明，朝着大规模量子信息处理的最终目标取得了令人印象深刻的技术成就。这些成就的核心是离子陷阱、激光和其他技术，这些技术在单个原子水平上提供了对实验参数的精确控制。利用这些技术，我们的目标是利用离子之间的相互作用--来自它们的库仑斥力以及陷阱和其他施加的电磁场--来研究多体物理，这种味道让人想起凝聚态中的熟悉模型。 我们的研究主要集中在激光冷却和俘获Yb离子阵列中的线性-之字形结构相变。这种转变的二阶性质，以及在实验装置中可以相对简单地控制它，构成了一个迷人的试验台，用于研究经典和量子制度、非线性动力学和非平衡统计力学中的介观相变。我们计划对Kibble-Zurek的拓扑缺陷形成机制进行测试，该机制改进了我们团队和其他人先前的实验，用于跨越线性-之字形转变的猝灭。我们还计划开拓新的方向，研究结构转变附近的离子晶体作为低维系统中热输运的可调模型，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，我们的目标是利用在跃迁附近形成的双势垒来控制离子晶体的两个之字形结构之间的隧道效应，实现一个让人想起氨分子的可调介观系统。 无论是量子力学的基础测试，还是模型材料的动力学研究，该计划都旨在推动囚禁离子的实验控制的极限。在这样做的过程中，由这笔赠款实现的技术将在相关的囚禁离子量子技术领域产生影响，甚至在任何正在研究信息的量子力学操纵的领域，例如量子信息处理、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.