Universal Few-Body Quantum States and Interactions

这个项目在许多方面推动了与我们国家利益相关的科学进步。这项工作将发展对一类涉及两个以上粒子的问题的理解，而目前的理论是非常有限的。具体来说，该小组将从三个或四个甚至更多粒子的相互作用中获得新的见解，这些粒子可能是原子、分子、核子甚至夸克。那些表面上截然不同的系统往往表现出一种普遍性，这意味着一个系统的某些方面非常相似，甚至在其他系统中也有反映。这项研究提出了一种最有前途的理论方法来解决这个困难的问题，这种方法是基于引入不寻常的集体坐标来描述系统的运动。一旦选择了最佳坐标，该项目就可以在现代计算机上实现量子力学方程，并提取精确的数值解。该项目应该产生对新现象的可信预测，以及可以提出进一步推进该领域研究的新途径的定性见解。这一努力也加强了能够解决微观世界中最具挑战性的理论问题的人才储备。本提案的研究计划建立在理解普遍少体物理学中当前有趣问题的进展之上，强调与超冷量子系统相关的应用。这个活跃的理论和实验领域已经看到了非常不寻常的束缚态和共振态，如所谓的Efimov效应，它也导致了理论方法的发展，例如绝热超球面表示，它能够定量描述涉及两到四个原子或分子的碰撞的非弹性碰撞和损失现象。该项目将解决这种超冷少体系统的复杂性的完整参数空间，无论是否有外部电磁场，都可以修饰系统并改变其特性。他们将努力克服处理四个以上原子的技术挑战，特别是积极推动处理五个原子。请注意，超冷量子气体物理将多个子领域的量子现象联系起来，特别是原子、分子、光学、凝聚态物质、核物理和化学物理。例如，对含有超冷原子的四费米子系统的了解，可以（并且已经）对四个相互作用的核子的核物理问题产生见解。该奖项反映了美国国家科学基金会的法定使命，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。

This project advances scientific progress in a number of ways that relate to our national interest. The work will develop an understanding of a class of problems involving more than just two particles where current theory is extremely limited. Specifically, the group will extract new insights into the interaction of three or four or even a few more particles, which might be atoms or molecules or nucleons or even quarks. Those apparently dramatically different systems often show a universality, meaning that some aspects of one system are very similar and are even mirrored in other systems. This research advances one of the most promising theoretical methods for attacking this difficult class, which is based on the introduction of unusual collective coordinates that describe the motions of the system. Once the best coordinates have been selected, the project can implement the quantum mechanical equations on modern computers, and extract accurate numerical solutions. The project should yield credible predictions of new phenomena, and also qualitative insights that can suggest new paths that further advance this field of research. The effort also strengthens the pool of talent capable of tackling the most challenging theoretical questions in the microscopic world.The research planned for this proposal builds on progress in understanding currently interesting problems in universal few-body physics, stressing applications relevant to ultracold quantum systems. This active theoretical and experimental field has seen highly unusual bound and resonant states, as in the so-called Efimov effect, and it has also led to the development of theoretical methods, such as the adiabatic hyperspherical representation, which are capable of quantitatively describing inelastic collision and loss phenomena for collisions involving two to four atoms or molecules. The project will address the full parameter space of complexity of such ultracold few-body systems, both with and without an external electromagnetic field that can dress the system and modify its properties. The efforts will work to overcome the technical challenges associated with treating more than four atoms, pushing aggressively to treat five atoms in particular. Note that ultracold quantum gas physics links quantal phenomena across multiple subfields, notably atomic, molecular, optical, condensed matter, nuclear physics, and chemical physics. What is learned about the four-fermion system with ultracold atoms, for instance, can yield (and has yielded) insights into the nuclear physics problem of four interacting nucleons.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.