Modeling, Analysis, Computation and Experiments of Two-Component Bose-Einstein Condensates

二元玻色-爱因斯坦凝聚体的建模、分析、计算和实验

• 批准号: 0806762
• 负责人: Ricardo Carretero
• 金额: $ 30万
• 依托单位: San Diego State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0806762&HistoricalAwards=false
• 关键词: Modeling; Analysis; Computation; Experiments; Two

CarreteroDMS-0806762 The goal of the project is to shed light on two-componentBose-Einstein Condensates (BECs) and how they differ from theirsingle-component counterparts. The investigator and hiscolleagues aim to redefine the way in which modeling and analysisare developed in such systems by introducing some fundamentalphysical processes that were not included in presently employedmodels. More specifically, the team of researchers plans to: (a) develop a new model for two-component BECs, by augmentingexisting models to account for processes such as inter-atomicinteraction losses and higher-order magnetic (Zeeman) effects; (b) benchmark the model, by testing it in a variety ofsituations where the total number of atoms or ratio of atomschanges between the two components and comparing it against thenewly developed partial differential equation model; (c) analyze the model mathematically by means of Galerkinprojections and Lyapunov-Schmidt reductions to study finitedimensional approximations of the dynamics, whereby the existenceand stability of solutions are studied and control strategies areemployed to stabilize potentially unstable solutionconfigurations; (d) produce a computational platform that enables the study ofexistence, stability and nonlinear dynamics of multi-component,high-dimensional variants of the nonlinear Schrodinger equationsthat are the key mathematical ingredient in the modeling of suchatomic systems. In the process, spatially/temporally adaptiveand/or parallel integrators are produced for time-steppingpurposes and iterative methods are developed in order to analyzethe linear stability problem around steady state solutions. This project presents a route to systematically quantify thequantum dynamics at the lowest temperatures that arise in theUniverse, namely in the recently created new form of matterrepresented by Bose-Einstein condensates (whose formation wasawarded with the 2001 Nobel prize in Physics and whoseproperties, such as superfluidity, were intimately connected tothe Nobel prize in Physics in 2003). The investigator and hiscolleagues form an interdisciplinary team to directly monitorthis state of matter in the laboratory, to model the system atthe physical level, to explore the resulting features at themathematical level, and finally to fully visualize thethree-dimensional dynamics of such complex systems. A continuousfeedback between all the above stages is intended to ascertainnot only a qualitative but also a quantitative understanding ofsuch atomic physics systems, such as gases of rubidium, sodiumand other alkali vapors. The multi-species systems under studypresent a wealth of opportunities for future applications,ranging from the controllable formation of ultracold microscopicpatterns (in a form of "quantum lithography") to the realizationof quantum gates and switches, that, in turn, aim towards thelonger term goal of enabling quantum computation.

CarreterOdms-0806762该项目的目标是阐明两种组件 - 核 - Einstein冷凝水（BEC），以及它们与他们的组件对应物的区别。 研究者和HisColleagues旨在通过引入一些未包含在当前使用的型号中的基本物理过程来重新定义在此类系统中建模和分析的方式。 更具体地说，研究人员团队计划：（a）通过增强Excististing模型来说明诸如原子间互动损失和高阶磁性（Zeeman）效应等过程，为两个组件BEC开发新的模型； （b）基准测试模型，通过在多种定位中对其进行测试，其中两个组件之间原子的总数或原子汇率的比率与当时开发的部分微分方程模型进行了比较； （c）通过数学分析模型通过GalerkinProjections和Lyapunov-Schmidt减少来研究动力学的有限少近似值，从而研究了解决方案的存在稳定性，并且控制了控制策略以稳定潜在的不稳定的解决方案求解; （d）产生一个计算平台，该平台能够研究非线性schrodinger方程的多组分，高维变体的稳定，稳定性和非线性动力学，这是该系统的建模中的关键数学成分。 在此过程中，为时间稳定的纯度生产了空间/时间上的适应性/或并行积分器，并开发了迭代方法，以分析围绕稳态解决方案的线性稳定性问题。 该项目提出了一种系统地量化Themiverse中最低温度的系统量化的途径，即以Bose-Einstein Condenses的最新形式创建的新形式的Matter Abressentes（其形成与2001年诺贝尔物理学奖和其诸如其诸如超级富度的奖励的形成均为，在2003年与诺贝尔物理奖密切相关）。 研究者和HisColleagues组成了一个跨学科的团队，可以直接监测实验室中物质的状态，以对物理层面进行建模，以探索Themathatematical层面的产生特征，最后完全可视化此类复杂系统的第三维动力学。 上述所有阶段之间的连续反馈旨在确定仅定性，而是对原子物理系统的定量理解，例如rubidium的气体，钠和其他碱性蒸气。 研究表现下的多物种系统为未来的应用提供了丰富的机会，从可控的超速显微镜形成（以“量子光刻”的形式）到实现量子门和开关的实现，又朝着thelonger Term tor Thelonger Term ok启用量子计算的目标。