Universal and Non-Universal Few-Body Physics in the Ultracold

从量子力学的早期开始，少体物理就在原子、分子和核物理中发挥了突出的作用。计划对具有多达6个粒子的超冷S波相互作用原子少体系统的普适和非普适方面进行微观描述。具体地说，发展了一种适用于具有有限轨道角动量的四体系统和五体系统的超球面显式关联高斯方法。与“标准”的显式关联高斯方法一起，该方法将被应用于具有各种对称性和大S波散射长度的少原子系统。此外，还将研究周期结构(周期盒子或光学晶格)中的少体系统的物理学。最后，将开发和应用微观有限温度方法。算法的开发有望对物理和化学中的各种子学科产生影响。将HCG方法成功地推广到有限角动量状态，有望提供获得单通道和多通道散射可观测值的途径。因此，所开发的方法除了在原子和分子物理中应用外，还可能在核和化学物理中得到应用。对超冷少体系统的应用将极大地增强我们对基本但高度关联的少体状态的理解，这些状态支配着超冷量子气体的大部分动力学。学生将积极参与拟议研究活动的所有方面，包括基础研究的规划、计算以及对结果的解释和论证。本科生和研究生在原子理论方面的研究培训，重点是分析和数值技术，为他们未来的广泛追求做好准备。学生的课堂体验将通过融入一些最新的进步而得到改善。

Few-body physics has played a prominent role in atomic, molecular and nuclear physics since the early days of quantum mechanics. A microscopic description of universal and non-universal aspects of ultracold s-wave interacting atomic few-body systems with up to six particles is planned. Specifically, a hyperspherical explicitly correlated Gaussian approach (HECG) applicable to four- and five-body systems with finite orbital angular momentum will be develoepd. Together with the "standard" explicitly correlated Gaussian approach, this approach will be applied to few-atom systems with various symmetries and large s-wave scattering lengths. Moreover, the physics of few-body systems in periodic structures (a periodic box or an optical lattice) will be investigated. Lastly, microscopic finite-temperature approaches will be developed and applied.The algorithm developments are expected to have implications for a variety of subdisciplines within physics and chemistry. The successful generalization of the HECG approach to states with finite angular momentum is expected to provide access to single- and multi-channel scattering observables. As such, the developed approach may find applications in nuclear and chemical physics, in addition to applications in atomic and molecular physics. The applications to ultracold few-body systems will significantly enhance our understanding of fundamental, yet highly correlated, few-body states, which govern much of the dynamics of ultracold quantum gases. Students will be actively involved in all aspects of the proposed research activities including the planning of the fundamental studies, the calculations and the interpretation and dissimination of the results. The research training of undergraduate and graduate students in atomic theory with emphasis on analytical and numerical techniques prepares them for a wide variety of future pursuits. Students' classroom experiences will be improved by incorporating some of the latest advances.