CAREER: Quantum Many Body Physics in Ultracold Atomic and Molecular Gases

提出了一种在量子力学前沿领域进行研究和教育的综合方法。研究部分集中在超冷气体中的量子多体理论和计算；教育部分集中于改革高级本科和研究生课程，从量子力学开始，与科罗拉多矿业学院正在进行的改进物理教育的广泛努力相一致。超冷量子气体的实验正在对物理和应用数学产生巨大影响，特别是在原子、分子和光学物理、凝聚态理论和非线性动力学方面。这些气体可以被捕获在任意结构的晶格中，所有参数都是动态和精确可控的，并且实验是100%无杂质的。因此，它们构成了一个设计的凝聚态系统，另外一个优点是，与典型的固态系统相比，微观参数是非常众所周知的。超冷费米子原子理论是一个特别重要的、迅速发展的跨学科研究领域。提出了三个主要的研究主题：量子相和Bardeen-Cooper-Schrieffer to Bose-Einstein凝聚(BCS-BEC)交叉；旋转晶格和其他奇异晶格构型和相；以及量子多体孤子和涡旋。每个主题的纯方面和应用方面都得到了解决。例如，利用费米对和玻色子之间的相干转换，求出了多带Fermi-Bose Hubbard哈密顿量的完整相图，它模拟了囚禁在任意维晶格势中的超冷费米子。在这项建议的教育方面，概述了对量子力学教育进行研究性改革的彻底努力。这项研究将与科罗拉多大学物理教育研究小组的诺亚·芬克尔斯坦和卡尔·威曼合作完成。量子力学的最新惊人发展，包括纠缠、退相干和量子信息的概念，将被纳入其中。作为物理教育技术项目的一部分，将开发和使用计算机模拟形式的量子力学物理演示，以及改进的教学技术，如在课堂上解决问题。

An integrated approach to research and education on the frontiers of quantum mechanics is proposed. The research portion focuses on quantum many body theory and computation in ultracold gases; the educational portion focuses on reforming the advanced undergraduate and graduate curriculum, beginning with quantum mechanics, in accord with the extensive ongoing efforts at improvement in physics education at the Colorado School of Mines.Experiments on ultracold quantum gases are having a huge impact on physics and applied mathematics, particularly in atomic, molecular, and optical physics, in condensed matter theory, and in nonlinear dynamics. These gases can be trapped in lattices of arbitrary structure, all parameters are dynamically and precisely controllable, and the experiments are 100% impurity free. Thus they constitute a designer condensed matter system, with the added advantage that the microscopic parameters are extremely well known in comparison to typical solid state systems. The theory of ultracold fermionic atoms is an especially important, rapidly expanding, interdisciplinary field of study. Three principal topics of research are proposed: quantum phases and the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS-BEC) crossover; rotating lattices and otherexotic lattice configurations and phases; and quantum many body solitons and vortices. Pure and applied aspects of each topic are addressed. For instance, it is proposed to find the complete phase diagram of a multi-band Fermi-Bose Hubbard Hamiltonian with coherent conversion between Fermi-pairs and bosons, which models ultracold fermions trapped in a lattice potential of arbitrary dimension. In the educational aspect of this proposal, a thorough effort at research-based reform of quantum mechanics education is outlined. This will be done in collaboration with Noah Finkelstein and Carl Wieman in the physics education research group at the University of Colorado. Recent spectaculardevelopments in quantum mechanics, including the concepts of entanglement, decoherence, and quantum information, will be incorporated. Quantum mechanics physics demonstrations in the form of computer simulations, as part of the Physics Education Technology Project, will be developed and used, as well as improved teaching techniques, such as problem solving in the classroom.