Few Level Models in Atomic Radiation Theory

这个研究项目涉及光与物质的基本相互作用，研究纠缠以及纠缠态如何随时间演变。纠缠指的是一种情况，在这种情况下，相隔很远的粒子无法相互独立地描述（或者，从数学上讲，当整体不等于各部分之和时）。利用数学模型来探索这些纠缠态是研究的一个重要方向。这可能有重要的应用，例如管理通信通道的安全性和量子信息科学。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实现。我们已经使用了分析和基于计算机的数学程序来进行纯态双分离的初步探索，但尚未发表。这些导致了对所谓的纠缠共享量子态空间的占用的限制。这些约束可以通过N维的简单体和多面体进行几何解释。随后对n方可加性的描述导致了纠缠共享关系，它们在一个新的方向上实质性地扩展了基于并发的结果，称为量子一夫一妻制。在重要但仍然简单的3个纠缠方的情况下，有三个双分离：b|bc， b|ac，和c b|ab，在这种情况下，由此产生的多面体是单位立方体内一对碱基对碱基的四面体。多面体与立方体对角线的横截面是三角形，我们发现它们的面积可以量化a、b、c三方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的和可行的，例如在宏观层面开发多模纠缠交换协议。

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.