Few Level Models in Atomic Radiation Theory

原子辐射理论中的几个能级模型

• 批准号: 1505189
• 负责人: Joseph Eberly
• 金额: $ 21万
• 依托单位: University of Rochester
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1505189&HistoricalAwards=false
• 关键词: Few; Level; Models; Atomic; Radiation

This research program deals with the basic interactions of light and matter, studying entanglement and how entangled states evolve in time. Entanglement refers to the situation in which widely separated particles cannot be described independently of each other (or, mathematically, when the whole is not equal to the sum of its parts). An important direction for the research is to use mathematical models to explore these entangled states. This may have important applications, for example in managing the security of communication channels and in quantum information science.The goal of the project is to develop a complete catalog of correlation relations among a large number N of fundamental physical systems (spins, atoms, photons). This will be done by the technical process of bi-separation of quantum states. We have used both analytic and computer-based mathematical procedures to carry out, but have not yet published, a preliminary exploration of pure state bi-separations. These lead to constraints on occupation of what can be called entanglement-shared quantum state space. These constraints have a geometrical interpretation via simplexes and polytopes in N dimensions. The consequent description of N-party additivity leads to entanglement sharing relations and they substantially extend in a new direction the concurrence-based results called quantum monogamy. In the important but still simple case of 3 entangled parties, there are three bi-separations: a|bc, b|ac, and c|ab, and the consequent polytope in this case is a pair of base-to-base tetrahedrons inside a unit cube. Cross sections of the polytope transverse to the body diagonal of the cube are triangles, and we have found that their areas serve to quantify the amount of entanglement sharing that is possible among the three parties a,b,c. Exchanges with the fields of quantum information and quantum optics appear desirable and feasible, for example in developing protocols for multi-mode entanglement swapping at the macroscopic level.

该研究项目涉及光和物质的基本相互作用，研究纠缠以及纠缠态如何随时间演化。 纠缠是指无法相互独立地描述相距较远的粒子的情况（或者，从数学上讲，当整体不等于其各部分的总和时）。研究的一个重要方向是利用数学模型来探索这些纠缠态。这可能有重要的应用，例如在管理通信通道的安全和量子信息科学中。该项目的目标是开发大量 N 个基本物理系统（自旋、原子、光子）之间相关关系的完整目录。 ）。这将通过量子态双分离的技术过程来完成。我们已经使用分析和基于计算机的数学程序来进行纯状态双分离的初步探索，但尚未发表。这些导致对所谓的纠缠共享量子态空间的占用的限制。这些约束通过 N 维的单纯形和多面体进行几何解释。 N 方可加性的后续描述导致了纠缠共享关系，并且它们在新的方向上实质上扩展了称为量子一夫一妻制的基于并发的结果。在重要但仍然简单的 3 个纠缠方的情况下，存在三个双分离：a|bc、b|ac 和 c|ab，在这种情况下，结果的多面体是内部的一对底对底四面体一个单位立方体。与立方体对角线垂直的多胞体横截面是三角形，我们发现它们的面积可以量化三方 a、b、c 之间可能共享的纠缠量。与量子信息和量子光学领域的交换似乎是可取且可行的，例如在宏观层面上开发多模纠缠交换协议。