Exploring Contacts in a New Era: Spin-Orbit Coupling and Dimension Crossover

物理学长期以来一直在努力寻求普遍规律。在经典力学中，牛顿定律可以解释大量的现象，包括苹果从树上掉下来和行星绕太阳运行。然而，在量子力学中，确定普遍的物理定律要困难得多，因为对于由许多相互作用的粒子组成的量子系统，求解薛定谔方程是非常困难的。这是不幸的，因为所有系统的大部分都是由许多相互作用的粒子组成的。 超冷原子为物理学家提供了一个很有前途的平台，以揭示量子世界中的普遍原理。由于平均粒子间距远大于电荷中性原子之间的相互作用范围，因此所谓的“接触”可以用来建立各种潜在的强大的普遍关系，这些关系无论超冷原子本身的微观参数如何都是有效的。这种普遍关系为物理学家理解和探索量子多体物理学提供了一种概念上的新方法。该项目将探索在超冷气体中使用“接触”，希望在多体系统中确定新的普遍关系。 最近的实验发展为物理学家提供了前所未有的机会来研究联系和宇宙关系。合成自旋轨道耦合已经在许多实验组中实现。这些新的耦合从根本上影响了多体波函数的短程渐近行为，并有望产生未探索的普遍关系。外俘获势可以连续地改变量子系统的维数。传统的结果得出的一个给定的尺寸不再适用于这样的维度交叉。这个项目的目的是使用自旋轨道耦合和维度交叉作为独特的工具，探索一个新的接触时代。主题包括提供新的普遍关系，工程非常规的有效哈密顿创造新的少体和多体状态，并实现接触作为一个新的计划跟踪量子多体现象。 该项目的成果将为使用接触来连接少体和多体物理学提供新的见解。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The pursuit of universal laws has been a long-term effort in physics. In classical mechanics, Newton's laws could explain a vast range of phenomena, including the falling of an apple from a tree and the orbiting of planets around the sun. In quantum mechanics, however, it is much more difficult to identify universal physical laws, since it is notably difficult to solve Schrodinger's equation for quantum systems composed of many interacting particles. This is unfortunate as the bulk of all systems consist of many interacting particles. Ultracold atoms provide physicists a promising platform to reveal universal principles in the quantum world. Due to the fact that the average particle-particle spacing is much larger than the range of interactions between charge-neutral atoms, the so-called "contacts" can be used to establish a variety of potentially powerful universal relations, which are valid regardless of microscopic parameters of the ultracold atoms themselves. Such universal relations bring physicists a conceptually novel means to understand and explore quantum many-body physics. This project will explore the use of "contacts" in ultracold gases in the hope of identifying new universal relations in many-body systems. Recent experimental developments offer physicists unprecedented opportunities to study contacts and universal relations. Synthetic spin-orbit couplings have been realized in many experimental groups. These novel couplings fundamentally influence the short-range asymptotic behavior of many-body wavefunctions and are expected to produce unexplored universal relations. External trapping potentials can continuously change the dimension of a quantum system. Traditional results derived for a given dimension no longer apply in such dimensional crossovers. This project aims to use spin-orbit coupling and dimensional crossover as unique tools to explore a new era of contacts. Topics include delivering new universal relations, engineering unconventional effective Hamiltonians for creating novel few- and many-body states, and implementing contacts as a new scheme for tracing quantum many-body phenomena. The outcome of this project will provide new insights into bridging few- and many-body physics using contacts.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.