Rare and Exotic Nonlinear Effects in Cold Atomic Gases

冷原子气体中罕见且奇异的非线性效应

• 批准号: 1402249
• 负责人: Maxim Olchanyi
• 金额: $ 21万
• 依托单位: University of Massachusetts Boston
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1402249&HistoricalAwards=false
• 关键词: Rare; Exotic; Nonlinear; Effects; Cold

Symmetries provide both means for unification of otherwise disparate branches of science and a language for communication between scientists and non-scientists. Two symmetries are prominent in this project: multidimensional kaleidoscopes and the quantum-mechanical supersymmetry that relates the motion with obstacles to the motion in free space. Through these symmetries some real physical effects---prohibition of chemical processes and slowdown of relaxation in waveguide-confined gases, transparency of solitary waves for other waves, etc---are tightly intertwined with tiling with polygons, Platonic solids, and cat-eye reflectors. The PI's presentation at the "Meet the Scientists!" at the Science Discovery Museum, entitled "Kaleidoscopes, tilings, Newton's cradles, and atoms at a billionth degree above absolute zero", scheduled for the beginning of May 2014, has effectively the same content as one of the three parts of this project. This project constitutes an indispensable pedagogical tool for training undergraduate and masters-level students. Each of the three sub-projects, while touching upon a range of advanced methods of modern theoretical physics, from Lie groups to quantum mechanical supersymmetry, does so gently, dealing with objects as graspable as ordinary differential equations. The sub-projects are also modular, divisible into several year-long smaller projects, and so ideal for an honors or MS thesis. Many qualitative ideas developed in the course of preparation for the project greatly contributed to the development of an undergraduate-oriented book.Nonlinear physics is famous for its archipelagoes of small under- or unexplored islands. The ultracold atomic gases are the ideal vehicle for visiting such islands. The nonlinear phenomena considered in this project are as follows: a protocol for an experimental generation of a Gross-Pitaevskii breather, in a waveguide for cold attractive bosons. (A further study will address the integrability-induced robustness of the chemical composition of one-dimensional Bose gases.); an analysis of the transparency of the Andreev-Bogoliubov-de Gennes BCS soliton to quasi-particles, using information previously acquired in a study of transparency of the Bogoliubov-de Gennes equations for known integrable partial differential equations. At the moment, it is not clear what physical phenomenon the BCS soliton transparency is supposed to enable, with the primary candidate being the Andreev reflection. A systematic study of quantum and classical cases of the three body scattering without diffraction associated with non-crystallographic and exceptional crystallographic root systems (kaleidoscopic mirror arangements) will also be performed. A particular sequence of mass triplets-with ( sqrt(5) + 2) : 1 : (sqrt(5) + 2) being the first nontrivial member that behave similarly to the Newton cradle will be identified. Here, the momentum distribution remains invariant under three-body collisions. The plan includes a systematic molecular-dynamics study of many-body mass mixtures, with masses controlled by optical lattices, with an expectation that the relaxation time will show peaks at the "extended Newton cradle" mass ratios.

对称性提供了统一原本不同的科学分支和科学家与非科学家之间交流的语言的手段。在这个项目中，两个对称性是突出的：多维万花筒和量子力学超对称性，将运动与障碍物与自由空间中的运动联系起来。 通过这些对称性，一些真实的物理效应 - - 禁止化学过程和在波导限制的气体中放松的放松，其他波浪的孤立波的透明度，等等----与多边形，柏拉图固体和cat-eye反射器紧密地交织在一起。 PI在“认识科学家”上的演讲！在科学发现博物馆中，题为“羽衣甘蓝，瓷砖，牛顿的摇篮和原子，以超过绝对零的十亿度”，计划于2014年5月初，实际上与该项目的三个部分中的一个相同的内容。该项目构成了培训本科生和硕士级学生的必不可少的教学工具。从谎言组到量子机械超对称性，这三个子项目中的每一个都在涉及一系列现代理论物理学的高级方法时，可以轻轻地处理与普通微分方程一样可掌握的对象。这些子项目也是模块化的，可分为几年的较小项目，因此非常适合荣誉或MS论文。在为该项目的准备过程中提出的许多定性思想极大地促进了一本面向大学的书籍。NonlinalearPhysics以其小型或未探索的小岛的群岛而闻名。超电原子气体是参观此类岛屿的理想工具。该项目中考虑的非线性现象如下：一种实验性生成的毛taevskii呼吸器的协议，在波导中，用于冷式有吸引力的玻色子。 （一项进一步的研究将解决一维玻色气体化学组成的整合性诱导的鲁棒性。）使用先前在Bogoliubov-de Gennes方程的透明度中获取的信息，对已知的可集成部分微分方程的透明度研究，对Andreev-Bogoliubov-de Gennes bcs soliton对准颗粒的透明度进行了分析。目前，尚不清楚BCS Soliton透明度应该可以实现哪种物理现象，主要候选人是Andreev反射。 还将对三种身体散射的量子和经典病例进行系统研究，而这些散射没有与非结晶和特殊晶体学根系（万花筒镜旋转）相关的衍射。带有质量三重态的特定序列（SQRT（5） + 2）：1 ：（ SQRT（5） + 2）是第一个与牛顿摇篮相似的非平凡成员。 在这里，在三体碰撞下，动量分布仍然不变。 该计划包括对多体质量混合物的系统分子动力学研究，其中由光学晶格控制，并期望放松时间在“扩展的牛顿摇篮”质量比下显示峰值。