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.

对称性既提供了统一不同科学分支的手段，也提供了科学家与非科学家之间交流的语言。该项目中有两个对称性很突出：多维万花筒和将障碍物运动与自由空间运动联系起来的量子力学超对称性。 通过这些对称性，一些真实的物理效应——化学过程的禁止和波导限制气体的弛豫减慢、孤立波对其他波的透明度等——与多边形、柏拉图固体和猫的平铺紧密地交织在一起。眼睛反射器。 PI 在“与科学家见面！”上的演讲计划于 2014 年 5 月初在科学探索博物馆举行，题为“万花筒、瓷砖、牛顿摇篮和绝对零以上十亿度的原子”，其内容实际上与该项目的三个部分之一相同。该项目是培养本科生和硕士生不可或缺的教学工具。这三个子项目中的每一个都涉及现代理论物理的一系列先进方法，从李群到量子力学超对称性，处理的对象就像常微分方程一样容易理解。这些子项目也是模块化的，可分为几个为期一年的较小项目，因此非常适合荣誉论文或硕士学位论文。在项目准备过程中形成的许多定性想法极大地促进了一本面向本科生的书籍的开发。非线性物理学以其未开发或未开发的小岛屿的群岛而闻名。超冷原子气体是游览这些岛屿的理想交通工具。该项目中考虑的非线性现象如下：在冷吸引玻色子的波导中实验生成 Gross-Pitaevskii 呼吸器的协议。 （进一步的研究将解决一维玻色气体化学成分的可积性引起的鲁棒性。）；使用先前在已知可积偏微分方程的 Bogoliubov-de Gennes 方程透明度研究中获得的信息，分析 Andreev-Bogoliubov-de Gennes BCS 孤子对准粒子的透明度。目前，尚不清楚 BCS 孤子透明度应该实现什么物理现象，主要候选者是安德烈夫反射。 还将对与非晶体和特殊晶体根系统（万花筒镜面排列）相关的无衍射的三体散射的量子和经典情况进行系统研究。将识别出质量三元组的特定序列，其中 ( sqrt(5) + 2) : 1 : (sqrt(5) + 2) 是第一个与牛顿摇篮行为相似的重要成员。 这里，动量分布在三体碰撞下保持不变。 该计划包括对多体质量混合物进行系统的分子动力学研究，质量由光学晶格控制，预计弛豫时间将在“扩展牛顿摇篮”质量比处显示峰值。