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

对普遍定律的追求是物理学的长期努力。在经典力学中，牛顿定律可以解释一系列现象，包括苹果从树上掉落，以及行星绕太阳运行。然而，在量子力学中，识别普遍的物理定律要困难得多，因为求解由许多相互作用的粒子组成的量子系统的薛定谔方程非常困难。这是不幸的，因为所有系统的主体都由许多相互作用的粒子组成。超冷原子为物理学家提供了一个很有前途的平台，来揭示量子世界中的普遍原理。由于平均粒子-粒子间距比电荷中性原子之间的相互作用范围大得多，所以所谓的“接触”可以用来建立各种潜在的强大的宇宙关系，这些关系是有效的，无论超冷原子本身的微观参数如何。这种宇宙关系为物理学家带来了一种概念上新颖的方法来理解和探索量子多体物理。这个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宇宙联系。最近的实验发展为物理学家提供了研究联系和宇宙关系的前所未有的机会。许多实验小组已经实现了合成自旋-轨道耦合。这些新颖的耦合从根本上影响了多体波函数的短程渐近行为，并有望产生未知的普遍关系。外陷陷势可以连续地改变量子系统的维度。针对给定维度得出的传统结果不再适用于这种维度交叉。该项目旨在使用自旋-轨道耦合和维度交叉作为独特的工具来探索接触的新时代。主题包括提供新的宇宙关系，设计非传统的有效哈密顿量来创建新的少体和多体状态，以及实现接触作为追踪量子多体现象的新方案。这一项目的结果将为使用接触联系连接少数和多体物理提供新的见解。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.