Few-Body Physics with Ultra Cold Atoms

超冷原子的少体物理

• 批准号: 1745142
• 负责人: Doerte Blume
• 金额: $ 14.83万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-05-16 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1745142&HistoricalAwards=false
• 关键词: Few; Body; Physics; Ultra; Cold

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.

大多数日常生活过程都受古典力学的约束。牛顿的第二个运动定律是一个众所周知的例子。在某些情况下，量子机械定律发挥了作用，经典定律不再提供对系统动力学的准确描述。量子机械定律已良好。但是，应用这些法律并做出定量预测是基本和技术重要性的一项高度挑战性的任务。 例如，元素性表和核图是量子机械考虑的结果，太阳能电池的工作原理也是如此。赠款支持的活动将大大提高我们对量子机械少体系统的理解。这些系统是更复杂的系统的原型。在可能的情况下，计划的理论研究将根据实验结果进行基准测试。作为该计划的一部分，将培训多个毕业生和本科生。这些学生将可以访问最先进的计算资源，并发展出强大的数值和分析能力。因此，他们将为学术界，国家实验室或行业的各种未来追求做​​好充分的准备。零温度，几个体型的相关性通常仅受几个参数的影响，例如两体S波散射长度和两体有效范围。这表明，可以利用有效的低能量汉密尔顿人来描述寒冷的几岁碰撞的关键方面和弱化的几个体状态。通过有效相互作用代替真实相互作用的想法类似于费米（Fermi）在他开创性的1934年论文中所做的关于慢速中子和结合氢原子之间的散射的想法。目前的赠款利用了冷原子物理学的实验和理论进步，并为冷几个原子系统的理论研究提供了支持。将开发并应用技术来解决不同类别的非平凡的少数身体系统的时间无关的Schrodinger方程，以便对几个粒子相关性和通用低能特征的更深入了解。分析方法包括围绕紧密耦合方案的扰动处理以及使用超级坐标方法的使用，可以看作是伯特·安萨兹（Bethe Ansatz）的陷阱类似物。数值技术包括基于Lippmann-Schinginger方程的治疗方法和使用明确相关的高斯人的基础扩展技术。