Spin and Spatial Correlations of Few-Body Systems

由几个孤立的被困原子组成的超冷系统允许以前所未有的控制程度研究量子关联和纠缠。利用分析和数值技术，该项目研究了这种超冷原子少体系统中空间位置和自旋之间的相关性。这些理论研究是与探索超冷物质的实验学家密切合作进行的。该项目旨在对不同原型量子系统中的相关性进行微观的、自下而上的理解，其中理论预测可以与实验结果相对照。物理学的这个分支的长期目标包括开发显著改进的成像系统和传感器，其可以具有广泛的应用。作为该项目的一部分，研究生和本科生将接受科学和技术领域的培训，目前在美国各地存在很高的需求。在进行这项研究的同时，学生将发展高性能计算的辅助技能。 第一项研究背后的想法是由海德堡Jochim小组正在进行的实验激发的，概念上很简单。在外部陷阱中准备一个初始的少费米子状态，然后通过削弱陷阱势来诱导膨胀，该小组将研究初始状态的相关性如何印在时间演化的波包上。他们将尝试开发方法来区分由粒子统计引起的“平凡”相关性和由短程接触相互作用引起的“非平凡”相关性。同样，他们将试图识别作为初始状态特征的相关性，并将它们与膨胀过程中产生的相关性进行对比。第二和第三个主题是相互关联的。他们考虑了存在人工规范场的超冷少原子系统，人工规范场在原子的自旋和线性动量之间引入了耦合。自旋-动量耦合导致非二次单粒子色散，这修改了振荡散射波函数和指数衰减束缚态波函数的大粒子间距离渐近性。第二个主题需要开发两个粒子散射框架的各种自旋动量耦合方案，占自旋和动量之间的相关性。预期的研究结果预计将显着修改标准教科书框架的分波散射。第三个课题是在自旋-动量耦合的情况下确定少原子态的束缚态谱和波函数。特别强调的是，将把在近阈值制度的相关性的增强。自旋-动量耦合是众多应用中的重要组成部分，包括（分数）拓扑绝缘体的研究、干涉测量和重力测量、自旋电子器件以及Majorana费米子的产生及其在量子计算机中的应用。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Ultracold systems comprised of a few isolated trapped atoms permit quantum correlations and entanglement to be studied with an unprecedented degree of control. Using analytical and numerical techniques, this project studies correlations between spatial positions and spins in such ultracold atomic few-body systems. These theoretical studies are conducted in close collaboration with experimentalists exploring ultracold matter. The project aims at developing a microscopic, bottom-up understanding of the correlations in different prototype quantum systems, where theoretical predictions can be confronted with experimental results. The long term goals of this branch of physics include the development of significantly improved imaging systems and sensors, which could have widespread applications. As part of this project, graduate and undergraduate students will be trained in science and technology areas, in which there currently exists a high demand across the US. While conducting this research, the students will develop subsidiary skills in high performance computing. The idea behind the first study, which is motivated by on-going experiments in Jochim's group in Heidelberg, is conceptually simple. Preparing an initial few-fermion state in an external trap and then inducing an expansion by weakening the trap potential, the group will study how correlations of the initial state get imprinted on the time-evolved wave packet. They will try to develop methods to distinguish between "trivial" correlations induced by the particle statistics and "non-trivial" correlations due to the short-range contact interactions. Likewise, they will try to identify correlations which are signatures of the initial state, and contrast them with those developed during the expansion. The second and third topics are interrelated. They consider ultracold few-atom systems in the presence of synthetic gauge fields, which introduce a coupling between the spin and the linear momentum of an atom. The spin-momentum coupling leads to non-quadratic single-particle dispersions, which modify the large interparticle-distance-asymptotics of oscillatory scattering wave functions and exponentially decaying bound state wave functions. The second topic entails developing two-particle scattering frameworks for various spin-momentum coupling schemes that account for the correlations between the spin and momentum. The anticipated findings are expected to significantly modify the standard textbook framework of partial wave scattering. The third topic entails determining bound state spectra and wave functions of few-atom states in the presence of spin-momentum coupling. Particular emphasis will be put on the enhancement of the correlations in the near-threshold regime. Spin-momentum coupling is an essential component in a myriad of applications including the study of (fractional) topological insulators, interferometry and gravimetry, spintronic devices, and the creation of Majorana fermions and their use in quantum computers.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.