Topological excitations in Bose-Einstein condensates: Existence, stability, dynamics, and interactions

玻色-爱因斯坦凝聚中的拓扑激发：存在性、稳定性、动力学和相互作用

• 批准号: 0505663
• 负责人: Ricardo Carretero
• 金额: $ 9.19万
• 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: 2005
• 资助国家: 美国
• 起止时间: 2005-07-15 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505663&HistoricalAwards=false
• 关键词: Topological; excitations; Bose; Einstein; condensates

Nonlinear media host a wide variety of localized coherent structures(solitons, wavetrains, vortices, spirals, etc.) with complex intrinsicproperties and interactions that, in turn, give rise to emergent patternswith nontrivial dynamics. The theme of the proposed research is a detailedexamination of vortices generated in dispersive nonlinear media.The main focus is to extend and deepen the understanding of vortexstructures, their existence and dynamical stability as well as theirinteractions and mesoscopic lattices in nonlinear media such asBose-Einstein condensates and related fields (such as nonlinear optics).We propose to follow a step-by-step methodology in studying thegeneration, stability and dynamics of vortices in a progression ofscenaria of increasing complexity, extending from single vortices, to few vortices, to vortex lattices. Specifically, we plan to study:(1) Vortex generation through dynamical instabilities and externalmanipulations such as phase imprinting and via instabilities driven byrapidly moving impurities (focused laser beams).(2) Dynamics and stability of single vortices (a.k.a. atoms) in thepresence of external traps and manipulation of vortices by translating theexternal traps or by using localized optical "tweezers".(3) Interactions between vortices and formation, stability and dynamicsof vortex dipoles (a.k.a. molecules/dipoles).(4) Finally, we intend to investigate, by cross-fertilizing ideas frommaterial science, large arrays of vortices, their crystallization andstructural phase transitions into regular vortex lattices (a.k.a. crystals).In the 1920's Bose and Einstein predicted that a gas at low density andultra-cold temperatures undergoes a transition towards what is nowadayscalled a Bose-Einstein condensate (BEC). The most important characteristicof a BEC is that all atoms occupy the same quantum state creating a macroscopiclump of coherent matter. BECs are to matter what laser is to light. BECs allowfor direct manipulation and observation of quantum effects at the macroscopiclevel, providing ultimate control over matter. Since their recentexperimental realization (for which the 2001 Physics Nobel prize wasgranted), BECs have been at the focus of an intensive and ever growingexperimental and theoretical effort. Vortices are fundamental coherent,topologically charged, nonlinear excitations that emerge in BECs; butwhich also play a profound role in exciting and important fields such assuperconductivity and superfluidity (which were the theme of the 2003Physics Nobel prize). Interestingly enough, they also arise in our dailylife in the form of hydrodynamic vortices in water or in air. There arestrong parallels (as well as differences) between such fluid vortices andthese ultra-cold, superfluid vortices that we plan to examine anddelineate. The outcome of this research will shed light into the patternformation and interaction of such vortex structures in Bose-Einsteincondensates. Since the underlying equation that describes the BECs alsodescribes the behavior of coherent light embedded in a nonlinearmaterial, the research hereby proposed will also be applicable toproblems of optical waveguides and fiber bundles, photonic crystals, andlight storage in optical traps, all of which are active research areas atthe forefront of optical technologies. The proposed research haspotential applications to quantum-optical storageand quantum computing for the next generation of computers.The research effort is part of an ongoing collaboration betweenthe PI and Co-PI and involves more than a dozen coworkers that blend inexpertise in fields as diverse as dynamical systems, nonlinear optics,condensed matter, materials science and scientific computing. Speciallyattractive is the prospect that our results will be partially driven andcould be relevant to current experimental research conducted in BECexperiments. This highly inter-disciplinary research program will alsoinvolve a major educational component through the direct involvement ofgraduate research assistants and postdoctoral fellows.

非线性培养基具有各种具有复杂的固有杂质和相互作用的局部相干结构（孤子，波浪，涡流，涡流，螺旋等），进而引起了新兴的模式。 The theme of the proposed research is a detailedexamination of vortices generated in dispersive nonlinear media.The main focus is to extend and deepen the understanding of vortexstructures, their existence and dynamical stability as well as theirinteractions and mesoscopic lattices in nonlinear media such asBose-Einstein condensates and related fields (such as nonlinear optics).We propose to follow a step-by-step methodology in studying涡流的涡流中的代，稳定性和动力学的复杂性增加，从单个涡流到几乎没有涡旋，再到涡旋晶格。具体而言，我们计划研究：（1）通过动态不稳定性和外部操作产生涡流的生成，例如相位烙印和通过易变的不动型杂质（聚焦激光束）驱动的不稳定性。 “镊子”。（3）涡旋与形成，稳定性和动力学之间的相互作用（又称分子/偶极子）。（4）最后，我们打算通过利用近距离科学的思想，大量的涡流和结构性相位的vortericals berex and to。爱因斯坦（Einstein）预测，低密度和硫酸冷气温下的气体经历了朝现象的bose-内施泰因冷凝物（BEC）的过渡。 BEC的最重要特征是，所有原子均占据相同的量子状态，从而产生了相干物质的宏观倾向。 Bec是重要的。 BEC允许直接操纵和观察巨大的量子效应，从而提供对物质的最终控制。自从他们最近的经验实现（2001年诺贝尔奖颁发了奖项）以来，BEC一直是一项密集且不断增长的经验和理论上的努力的重点。涡旋是基本的连贯性，拓扑充电，在BEC中出现的非线性激发。但是，这在令人兴奋和重要的领域中也发挥了深远的作用，例如实力和超流动性（这是2003年诺贝尔奖的主题）。有趣的是，它们在我们的Dailylife中也以水或空气中的流体动力涡流形式出现。我们计划检查和二元组之间的这些流体涡流和这些超冷的超氟涡流之间的Arestrong（以及差异）。这项研究的结果将阐明Bose-Einsteconconcondates中此类涡流结构的模式形式和相互作用。由于描述BEC的基础方程式嵌入了非线性材料中的相干光的行为，因此此处的研究还将提出的研究还适用于光学波导和纤维捆，光子晶体，光子晶体，并在光学上的储存中，并在光学陷阱中均具有活跃的研究区域，这些储存是光学研究领域的。拟议的研究对下一代计算机的量子 - 光学量子计算具有潜在的应用。研究工作是在PI和Co-Pi上进行的持续合作的一部分，并参与了多个多数的同事，这些同事将其融合在领域中，以多样化的范围为动态系统，非线性的Aseal Aseal Optics，非线性的光学，凝结物质，材料，材料，材料，科学，材料，科学和科学计算。特别突出的是，我们的结果将部分驱动，并应与当前在Beceppermiments进行的实验研究有关。这项高度跨学科的研究计划还将通过直接参与研究生研究助理和博士后研究员来为主要的教育组成部分。