Universal Few-Body Quantum States and Interactions

该项目以与我们国家利益相关的多种方式推动科学进步。 这项工作将发展对一类问题的理解，这些问题涉及的不仅仅是两个粒子，而目前的理论非常有限。 具体来说，该小组将对三个或四个甚至更多粒子的相互作用提出新的见解，这些粒子可能是原子或分子或核子，甚至是夸克。 这些明显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。这项研究提出了一个最有前途的理论方法来攻击这个困难的类，这是基于引入不寻常的集体坐标，描述系统的运动。一旦选定了最佳坐标，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。该项目应该产生新现象的可靠预测，以及可以提出进一步推进这一研究领域的新途径的定性见解。 该计划的研究将建立在对当前宇宙少体物理学中有趣问题的理解上，重点关注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，如在所谓的Efimov效应中，它也导致了理论方法的发展，如绝热超球表示，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复杂性的完整参数空间，无论是否有外部电磁场可以修饰系统并修改其属性。这些努力将致力于克服与处理四个以上原子相关的技术挑战，特别是积极推动处理五个原子。 请注意，超冷量子气体物理学将量子现象跨多个子领域联系起来，特别是原子，分子，光学，凝聚态，核物理和化学物理。例如，对超冷原子的四费米子系统的了解可以（并且已经）产生对四个相互作用核子的核物理问题的见解。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。

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.