Few-Body Physics with Ultra Cold Atoms

大多数日常生活过程都是由经典力学支配的。牛顿第二运动定律就是一个众所周知的例子。在某些情况下，量子力学定律开始发挥作用，经典定律不再提供对系统动力学的准确描述。量子力学定律得到了很好的确立。然而，应用这些规律并做出定量预测是一项具有重大基础和技术意义的极具挑战性的任务。例如，元素周期表和核图是量子力学考虑的结果，太阳能电池的工作原理也是如此。该基金资助的活动将极大地促进我们对量子力学少体系统的理解。这些系统作为更复杂系统的原型。在可能的情况下，计划中的理论研究将以实验结果为基准。作为该计划的一部分，将对多名研究生和本科生进行培训。这些学生将获得最先进的计算资源，并将发展强大的数值和分析技能；因此，他们将为未来在学术界、国家实验室或工业中的各种追求做好准备。在接近零度的温度下，少体关联往往只受几个参数控制，如二体S波散射长度和二体有效射程。这表明有效的低能少原子哈密顿量可以用来描述冷少体碰撞和弱束缚少体状态的关键方面。用有效的相互作用取代真正的相互作用的想法类似于费米在1934年关于慢中子和束缚氢原子之间的散射的开创性论文中所做的工作。目前的拨款充分利用了冷原子物理学的实验和理论进展，并为冷原子系统的理论研究提供了支持。将开发和应用技术来求解不同类型的非平凡少体系统的与时间无关的薛定谔方程，目的是加深对少粒子关联和普遍低能特征的理解。分析方法包括围绕强耦合区域的微扰处理，以及可被视为类似Bethe ansatz的陷阱的超球面坐标方法的使用。数值技术包括基于Lippmann-Schwinger方程的处理和利用显式相关高斯的基集扩展技术。

Most every-day life processes are governed by classical mechanics. Newton's second law of motion is a well-known example of this. In certain situations, quantum mechanical laws come into play and the classical laws no longer provide an accurate description of the system dynamics. The quantum mechanical laws are well established. However, applying these laws and making quantitative predictions is a highly challenging task of fundamental and technical importance. The periodic table and nuclear chart, for example, are the result of quantum mechanical considerations, as are the working principles of solar cells. The activities supported by the grant will greatly advance our understanding of quantum mechanical few-body systems. These systems serve as prototypes for more complex systems. Where possible, the planned theoretical studies will be benchmarked against experimental results. As part of this program, multiple graduate and undergraduate students will be trained. These students will have access to state-of-the-art computing resources and will develop strong numerical and analytical skills; thus, they will be well prepared for a variety of future pursuits in academia, at national labs or in industry.Near zero temperature, few-body correlations are often times governed by just a few parameters such as the two-body s-wave scattering length and the two-body effective range. This suggests that effective low-energy few-atom Hamiltonians can be utilized to describe the key aspects of cold few-body collisions and of weakly-bound few-body states. The idea of replacing the true interactions by effective interactions is similar to what Fermi did in his groundbreaking 1934 paper on the scattering between slow neutrons and bound hydrogen atoms. The present grant capitalizes on experimental and theoretical advances in cold atom physics and provides support for theoretical studies of cold few-atom systems. Techniques will be developed and applied to solve the time-independent Schrodinger equation for different classes of non-trivial few-body systems, with the goal of developing a deeper understanding of few-particle correlations and universal low-energy features. The analytical approaches include perturbative treatments around the strongly-coupled regime and the use of a hyperspherical coordinate approach that can be viewed as a trap analog of the Bethe ansatz. Numerical techniques include a Lippmann-Schwinger equation based treatment and a basis set expansion technique that utilizes explicitly correlated Gaussians.