Temperature Dependence and Dynamics of Cold Few-Atom Systems

要在量子水平上实现对物质的控制，需要在量子水平上详细了解多体系统。这一项目有望加强对具有根本重要性的量子力学过程的理解，特别是对费米原子的超冷少体系统的热力学性质的理解。最终，从自下而上的角度理解量子力学现象将对从改进的手机技术到改进的手术工具等广泛的日常任务具有重要的技术意义。当今世界是技术驱动的世界，需要高技能的劳动力。这个项目将培养下一代青年科学家。本科生和研究生将参与该项目的所有方面，学生获得的分析和计算技能将为他们未来在工业和学术界的追求做好准备。这个项目将通过开发数值和分析工具来推动科学发展，这些工具允许研究量子力学少体系统的温度相关性和动力学。少体物理从一开始就在量子力学的发展中扮演着重要的角色。例如，氦原子是元素周期表中最简单的原子之一，也是一个有效的三体系统，在发展对电子-电子关联以及碎裂和(自动)电离的简洁理解方面发挥了重要作用。由少量粒子(二、三、四等)组成的超冷费米子气体的实验实现为研究零温和有限温度下的量子力学少体现象提供了一种新的理论上可行的模型系统。此外，与时间相关的测量结果可以直接与理论预测进行比较。该项目旨在对冷的少原子系统进行理论研究。利用研究人员开发的一种有效而灵活的路径积分蒙特卡罗程序，将对捕获的少原子系统进行有限温度计算，该程序已被证明在很宽的温度范围内对小玻色子和费米子系统产生可靠的结果。路径积分蒙特卡罗代码将作为软件重用风险基金计划的一部分提供给更广泛的科学界。时间相关的研究将使用一种高效和高精度的基于网格的时间传播方案来执行，该方案根据切比雪夫多项式来扩展时间演化算子。

Achieving the control of matter at the quantum level requires the detailed understanding of many-body systems at the quantum level. This project is expected to enhance the understanding of quantum mechanical processes of fundamental importance, in particular the thermodynamical properties of ultracold few-body systems of fermionic atoms. Ultimately, understanding quantum mechanical phenomena from a bottom-up perspective will have important technological implications for a wide range of every-day tasks ranging from improved cell phone technology to improved surgical tools. Today's world is technology driven and requires a highly skilled workforce. This project will train the next generation of young scientists. Undergraduate and graduate students will be involved in all aspects of the project, and the analytical and computational skills that the students gain will prepare them well for future pursuits in industry and academia. This project will advance science by developing numerical and analytical tools that allow for the study of the temperature dependence and dynamics of quantum mechanical few-body systems. Few-body physics has played an important role in the development of quantum mechanics from the very beginning. For example, the helium atom, one of the simplest atoms of the periodic table and an effective three-body system, has been instrumental in developing a concise understanding of electron-electron correlations as well as fragmentation and (auto-) ionization. The experimental realization of ultracold fermionic gases consisting of a small number of particles (two, three, four, etc.) provides a new theoretically accessible model system with which to study quantum mechanical few-body phenomena at zero and finite temperature. Moreover, time-dependent measurements can be compared directly with theoretical predictions. This project aims to conduct theoretical studies of cold few-atom systems. Finite-temperature calculations for trapped few-atom systems will be performed using an efficient and flexible path-integral Monte Carlo code developed by the investigator, which has been shown to yield reliable results for small bosonic and fermionic systems over a wide range of temperatures. The path-integral Monte Carlo code will be made available to the broader scientific community as part of the Venture Fund for Software Reuse program. Time-dependent studies will be performed using an efficient and highly accurate grid-based time propagation scheme that expands the time evolution operator in terms of Chebychev polynomials.