RUI: Ultracold Atoms in Ring-Shaped Lattices

由于对原子、分子和光子系统的控制显著增强，预计未来几年熟悉的技术将发生剧变。在这些预期的革命中，传感器技术将影响到广泛的设备，这些设备通常用于检测和测量电流、磁场和引力场、光强度等一切，仅举几个例子。推动这些发展的关键因素是量子纠缠，即即使是相隔很远的量子系统的可观察属性之间的奇怪关联。虽然纠缠在量子系统中无处不在，但它也非常微妙，并且可以被量子系统与其环境的相互作用所改变或破坏。正是这种微妙之处，使得精确控制的量子系统成为潜在的革命性传感器技术的源泉。这个项目涉及的是由束缚在环形陷阱中的纠缠超冷原子形成的简单传感器。环形结构允许反向传播的物质波干涉，形成一种对原子间相互作用具有高度灵敏度的干涉仪。研究结果在量子信息处理和新型量子材料方面的其他应用也将被探索。该项目将在一所低成本大学积极培训和吸引众多本科生参与物理研究，并扩大在先前资助下取得的成功，利用这一经验引导学生进入STEM职业道路，包括许多来自代表性不足的人口统计数据。具体来说，该项目将对被困在具有多重连接的全局拓扑结构的晶格中的超冷原子所能实现的现象进行全面研究，例如环、圆柱体或环面。非平凡拓扑通过规范场或旋转引入了包含有效通量的周期和扭曲边界条件，并揭示了量子态的相干和非局域特征。在这一总体背景下，将审查范围广泛的主题。环形几何模型在理解非相对论物理中拓扑和规范自由的影响方面起着至关重要的作用。这项研究将发展和扩展这些模型，使其在冷原子中可行地实现，以探测当这些模型被设想时通常无法实现的场景。所研究的现象将包括人工规范场、量子霍尔效应、任意子物理、量子泵、霍夫施塔特模型、阿哈罗诺夫-玻姆和几何相位效应。可以绕过不确定性限制的自旋压缩和非线性动力学将在共享相同物理空间的原子的反循环集体模式的新背景下进行检查。在可能的情况下，这些现象将随着时间和空间的演变而动态地加以检验，并注意到时间可以增加或替代其他自由度。将环视为人造原子，对于通常与内部自由度有关的现象，将在外部自由度中建立对应的环。

Upheavals of familiar technologies are expected in coming years due to the dramatically enhanced control of atomic, molecular and photonic systems. Among these anticipated revolutions is that in sensor technology, affecting a wide array of devices regularly used to detect and measure everything from electric currents, magnetic and gravitational fields, and light intensities, to name a few examples. The key element driving these developments is quantum entanglement, the strange correlations between observable properties of even widely-separated quantum systems. While entanglement is ubiquitous in quantum systems, it is also extremely delicate, and can be altered or spoiled by interactions of the quantum system with its environment. This delicacy is precisely what makes exquisitely controlled quantum systems the source of potentially revolutionary sensor technology. This project concerns simple sensors formed by entangled ultracold atoms confined in ring-shaped traps. The ring-shape allows for the interference of counter-propagating matter waves, forming a kind of interferometer which has exquisite sensitivity to interactions between the atoms. Additional applications of the results to quantum information processing and to new quantum materials will also be explored. The PI will actively train and involve numerous undergraduate students in physics research at a low cost university, and expand on success under prior grants to leverage this experience to channel students into STEM career paths, including many from under-represented demographics. Specifically, this project will conduct a comprehensive study of phenomena realizable with ultracold atoms trapped in lattices with a global topology that is multiply-connected, such as rings, cylinders or tori. The non-trivial topology naturally introduces periodic and twisted boundary conditions with the inclusion of effective flux via gauge fields or rotation, and reveals coherent and non-local features of quantum states. Within this general context, a broad range of topics will be examined. Models with ring-shaped geometry have played a crucial role in understanding the influences of topology and gauge freedoms in non-relativistic physics. This research will develop and extend those models for viable implementation with cold atoms to probe scenarios often inaccessible when such models were conceived. The phenomena to be so studied will include artificial gauge fields, quantum Hall effect, anyon physics, quantum pumps, Hofstadter model, and Aharonov-Bohm and geometric phase effects. Spin-squeezing, that can bypass uncertainty limits, and nonlinear dynamics will be examined in the novel context of counter-circulating collective modes of atoms sharing the same physical space. Where possible, the phenomena will be examined dynamically with evolution in time and space, noting that time can add or substitute for other degrees of freedom. Treating rings as artificial atoms, counterparts will be established in external degrees of freedom for phenomena usually associated with internal ones.