Topological Solitons in Liquid Crystals and Colloids

非技术性胶体在自然界、科学和技术中都很丰富，从牛奶到量子计算感兴趣的量子点。同样，液晶有序在从生物膜到消费设备显示器的各种环境中都很重要。在液晶显示器的每个像素中，棒状分子的方向都受到低压电场的旋转，从而可以控制透射光随意传递信息。这种灵巧的电子开关是每年5000亿美元全球液晶产业的核心，它处理的是棒状分子分子排列场中非常简单、均匀和连续扭曲的结构。PI和他的团队研究如何控制液晶来容纳这种分子排列场的打结图案。他们研究分散在液晶中的细小的棒状和盘状胶体颗粒，以开发一本将颗粒组织成精确可控结构的“配方书”。电场和磁场可以与这些结构相互作用，打结或解开它们，这可能会丰富液晶控制光的手段。这项研究可能会导致对社会具有重要意义的应用，如新品种的显示器、波束转向和数据存储设备。PI将这项研究与广泛的协同教育和推广活动结合在一起，包括为学校教师和学生提供展示和科学之旅，为专业协会的学生分会提供建议，为少数族裔服务机构的学生提供研究经验，为本科生和博士研究人员提供建议，教授液晶行业的会议课程，参与访问讲师计划以及组织会议和暑期学校。TECHNICAL ABSTRACTPI探索了各向异性液晶分子和胶体纳米颗粒通过拓扑控制自组装成拓扑独特的孤子配置的基本组织原理，这些孤子配置比分子和纳米颗粒大数千到数百万倍。被广泛研究的磁天空微子是具有空间局域拓扑保护的连续磁化绕组的二维孤子。3D Skyrmions(Hopfions)在所有三个空间维度上都是局域化的，并由Hopf指数来表征，Hopf指数是一个拓扑不变量，它对任意两个闭环系统前像的链接数量进行几何解释，空间中具有相同场方向的区域对应于序参数空间上的单个点，例如磁化矢量场的单位球。PI发展了一种新型的可调液晶结构，具有复杂但可预测的拓扑结构对外场的响应以及传播的光孤子和激光束的涡旋。利用激光镊子、三维非线性光学成像和视频显微镜的组合来控制和探测2D和3D孤子之间的平衡自组装和动态相互作用。这项跨学科的工作解决了凝聚态物理、拓扑学、纳米科学和光子学界面上的关键问题。在这些领域的交汇点上，新兴的科学前沿显示出新发现和应用的非凡前景。这项工作推进了我们对三维拓扑孤子结构和动力学的基础知识，扩展了复杂流体中自组装现象的多样性，并冲击了胶体相互作用、拓扑、非线性和奇异光学、全光信息处理等科学领域的基础知识。除了作为基础研究的模型系统外，所研究的孤子的潜在技术用途还包括光束操纵装置、用于奇异光学应用的光学涡旋发生器、具有强大的光偏振控制能力的光学电路，以及在材料中形成晶体和其他晶格的具有结合场配置的拓扑学上的非平凡孤子。在过去教育和外展成就的基础上，PI将这项研究与广泛的协同活动相结合，从培训学生和为非科学家提供教学课程，到通过科罗拉多大学周六物理讲座和巫师展示向公众和儿童传达科学兴奋。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

NON-TECHNICAL ABSTRACTColloids are abundant in nature, science and technology, with examples ranging from milk to quantum dots that are of interest for quantum computing. Similarly, liquid crystal ordering is important in contexts ranging from biological membranes to displays in consumer devices. In every pixel of a liquid crystal display, the direction of rod-like molecules is rotated by a low-voltage electric field, so that the transmitted light can be controlled to convey information at will. This facile electric switching, which is at the heart of $500 billion per year global liquid crystal industry, deals with very simple uniform and continuously distorted structures of the molecular alignment field of rod-like molecules. The PI and his team study how liquid crystals can be controlled to host knotted patterns of this molecular alignment field. They study tiny rod-like and disc-like colloidal particles dispersed in a liquid crystal to develop a "recipe book" for organizing particles into precisely controlled structures. Electric and magnetic fields can interact with these structures, knotting or unknotting them, which may enrich the means of controlling light by liquid crystals. This research may lead to applications of importance to society, such as new breeds of displays, beam steering and data storage devices. PI combines this research with a broad range of synergistic educational and outreach activities, including shows and science tours for school teachers and students, advising student chapters of professional societies, providing research experiences for students from minority-serving institutions, advising undergraduate and PhD researchers, teaching conference courses for liquid crystal industry, participation in visiting lecturer programs and organization of conferences and summer schools.TECHNICAL ABSTRACTPI explores the fundamental organizing principles behind topology-dictated self-assembly of anisotropic liquid crystal molecules and colloidal nanoparticles into topologically distinct soliton configurations that are thousands-to-millions times larger than molecules and nanoparticles. Widely studied magnetic skyrmions are 2D solitons with a spatially localized topology-protected continuous winding of magnetization. 3D skyrmions (hopfions) are localized in all three spatial dimensions and characterized by the Hopf index, a topological invariant with a geometric interpretation of the linking number of any two closed-loop preimages, regions in space with the same orientation of field corresponding to a single point on the order parameter space, such as a unit sphere for the magnetization vector field. PI develops a new breed of tunable liquid crystal structures with complex but predictable topology-dictated response to external fields and propagating optical solitons and vortices of laser beams. Both equilibrium self-assembly and dynamic interactions between 2D and 3D solitons are controlled and probed using a combination of laser tweezers, 3D nonlinear optical imaging, and video microscopy. This interdisciplinary work addresses key problems at the interfaces of condensed matter physics, topology, nanoscience and photonics. The emerging scientific frontiers at the nexus of these fields show exceptional promise of new discovery and applications. This work advances our fundamental knowledge of structure and dynamics of 3D topological solitons, expands the diversity of self-assembly phenomena in complex fluids and impinges on fundamental knowledge in scientific fields as diverse as colloidal interactions, topology, nonlinear and singular optics, all optical information processing, and other. In addition to serving as a model system for fundamental studies, potential technological uses of the studied solitons include beam steering devices, generators of optical vortices for singular optics applications, optical circuitry with robust capabilities of controlling polarization of light, and topologically nontrivial solitons with knotted field configurations forming crystalline and other lattices in materials. Building on his past education and outreach accomplishments, the PI integrates this research with a broad spectrum of synergistic activities, ranging from training of students and teaching courses for non-scientists to conveying the scientific excitement to public and children through the University of Colorado Saturday Physics Lectures and Wizard Shows.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.