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

自量子力学早期以来，少体物理在原子、分子和核物理中起着突出的作用。计划对具有多达六个粒子的超冷s波相互作用的原子少体系统的普遍和非普遍方面进行微观描述。具体来说，将发展一种适用于四体和五体系统的轨道角动量有限的超球面显式相关高斯方法（HECG）。与“标准”显式相关高斯方法一起，该方法将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，将研究周期结构（周期盒或光学晶格）中少体系统的物理性质。最后，微观有限温度方法将得到发展和应用。预计算法的发展将对物理和化学中的各种分支学科产生影响。将HECG方法成功地推广到具有有限角动量的状态，有望提供对单通道和多通道散射观测的访问。因此，所开发的方法除了在原子和分子物理方面的应用外，还可以在核物理和化学物理方面得到应用。在超冷少体系统中的应用将大大提高我们对基本的、但高度相关的少体态的理解，这些状态控制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各个方面，包括基础研究的规划、计算以及结果的解释和传播。本科生和研究生在原子理论方面的研究训练，重点是分析和数值技术，为他们将来的各种追求做好准备。学生的课堂体验将通过结合一些最新的进展而得到改善。

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.