Topological Quantum Hydrodynamics in Nonmetallic Materials

非技术总结该奖项支持理论研究和教育，旨在揭示绝缘材料的隐藏物理性质和潜在用途。这些材料可以是化学上自然的，也可以是以原子层层方式明智地定制的。基本元素之间的动态协作可以导致有效地打结的几何实体，例如类似刺头上脊椎排列的漩涡或磁性纹理，这会刺激意想不到的物理行为。在某些天然或工程系统中，复杂的几何特征已经编织到均匀材料本身的化学结构中。虽然这可能不是直接明显的，但它可以通过材料边界的奇异物理来体现。后者又可以通过对边缘进行电、热或光学操作来控制整体上的纹理非均匀动力学。最终，这项研究旨在通过适当设计的系统和设备来建立经典和量子信息传输的新模式，这些系统和设备可以展示新类型的(非平衡)动力学和(非电)信号产生，以及产生隐藏的功能。因此，这里研究的主题具有技术含义，同时也提供了教育机会。PI与材料科学家和工程师的合作将促进高效纳米级能量存储和量子通信的新设备概念。拓扑学、量子传输学和量子信息科学的交叉也为设计现代课程、培养学生和博士后的研究课题以及面向学校和公众的教育拓展提供了一个极好的出发点。PI将与加州纳米系统研究所合作，在洛杉矶公立学区开展外联活动，在加州大学洛杉矶分校的暑期实习计划中保持理论纳米科学部分，并为他所在部门定期向公众提供的物理展会做出贡献。除了加州大学洛杉矶分校，还将为来自发展中国家的科学家组织一次国际会议，讨论凝聚态物理中的拓扑和量子现象。技术总结该奖项支持理论研究和教育，以研究具有拓扑特征的材料中新的信息流模式和相关的量子关联。后者通常与整体边界对应联系在一起，并通过对系统边界的操纵和测量来控制系统内部的动力学和传输过程。我们主要对绝缘磁或超导系统感兴趣，它们可以表现出不受太多耗散阻碍的空间非均匀序参数动力学。这种集体织构背后的拓扑守恒定律，如2D中的磁性/超导涡度或3D中的磁性刺猬织构，为发展量子输运的系统场论形式提供了一个流体力学框架。拓扑体-边界关系能够偏置和测量热电或光学上的拓扑织构流动，为探测各种类型的非金属介质中的输运提供了一种全新的途径。在发展了微观量子响应理论之后，它将被应用于有序、无序和临界区的有效描述，重点是量子磁体和自旋液体。即使对于普通的铁磁体和反铁磁体，我们的观点也提出了询问材料的新类型的问题。当材料在其能带结构水平上已经是拓扑的时候，这变得更加有趣，就像在量子霍尔相和拓扑超导体中一样。在这里，我们期待两个相互交织的整体边界特征，由带状结构拓扑决定的健壮的边缘状态为我们提供了在整体上偏向和控制真实空间拓扑纹理的通用手段。低能量子自由度，无论是自然地与拓扑特征相关的(如涡旋核中的Skrmionic振动或Majorana费米子)，还是人工注入的(如钻石中的氮空位中心)，然后与离域集体驱动耗散动力学相结合地研究。这个项目将从三个方面加深我们对相关量子材料的基本性质的理解：(I)通过棱镜的基于拓扑守恒定律的新的输运性质(到目前为止在固态中一直没有引起太多关注)；(Ii)通过将可单独访问的量子比特集合调整为与拓扑材料的强(电磁)耦合，并量化诱导的纠缠；以及(Iii)探索驱动耗散动力学的这些问题，其中非厄米性质丰富了拓扑性质和相关的量子关联。因此，该项目旨在提供相关材料动态性质的新的通用探测器，关注拓扑、量子纠缠和耗散以及它们之间的相互作用。这一奖项反映了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。

NONTECHNICAL SUMMARYThis award supports theoretical research and education with an aim to unravel hidden physical properties and potential utilities of insulating materials. These materials could be chemically natural or judiciously tailored in an atomic layer-by-layer fashion. The dynamic cooperation among the underlying elementary constituents can result in the effectively knotted geometric entities, such as vortices or magnetic textures that resemble the arrangement of spines on a hedgehog, that spur unexpected physical behavior. In certain natural or engineered systems, an intricate geometric character is already woven into the chemical fabric of the homogeneous material itself. While this may not be directly evident, it can be manifested through exotic physics at the material's boundary. The latter, in turn, can be exploited to control the textured inhomogeneous dynamics in the bulk by electrical, thermal, or optical manipulations on the edges. Ultimately, this research aims at establishing new modalities for classical and quantum information transmission by appropriately designed systems and devices, which can exhibit novel types of (out-of-equilibrium) dynamics and (nonelectrical) signal generation as well as yield hidden functionalities.The topics studied here thus have technological implications, while also offering educational opportunities. The PI's collaboration with materials scientists and engineers will promote new device concepts for efficient nanoscale energy storage and quantum communications. The intersection between topology, quantum transport, and quantum information science also offers a terrific departure point for designing modern courses, research topics for training students and postdocs, as well as educational outreach to schools and the public. The PI will team up with the California NanoSystems Institute to carry out outreach activities to Los Angeles public school district, maintain a theoretical nanoscience component at the UCLA summer internship programs, as well as contribute to the physics fairs that are periodically offered to the public by his department. Beyond UCLA, an international conference will be organized for scientists from developing nations, with a broad scope in topological and quantum phenomena in condensed-matter physics.TECHNICAL SUMMARYThis award supports theoretical research and education to investigate novel modes of information flow and the associated quantum correlations in materials with topological character. The latter is generally associated with bulk-boundary correspondence, and provides control handles on the dynamics and transport processes in the interior of a system through the manipulations and measurements on its boundaries. We are primarily interested in insulating magnetic or superconducting systems, which can exhibit spatially-inhomogeneous order-parameter dynamics not hindered by much dissipation. Topological conservation laws underlying such collective textures, like magnetic/superconducting vorticity in 2D or magnetic hedgehog textures in 3D, offers a hydrodynamic framework for developing a systematic field-theoretic formalism for quantum transport. The topological bulk-boundary relations enable the bias and measure the topological texture flow, either thermoelectrically or optically, offering a fundamentally new way to probe transport in wide classes of nonmetallic media. After developing a microscopic quantum response theory, it will be applied to effective descriptions for ordered, disordered, and critical regimes, with a focus on quantum magnets and spin liquids. Even for ordinary ferromagnets and antiferromagnets, our perspective raises new types of questions for interrogating materials. This becomes even more interesting when the material is already topological at the level of its band structure, as in the quantum Hall phases and topological superconductors. Here, we anticipate two interwoven bulk-boundary features, with the robust edge states dictated by the band-structure topology affording us universal means to bias and control real-space topological textures in the bulk. Low-energy quantum degrees of freedom, which are either naturally associated with the topological features (such as skyrmionic vibrations or Majorana fermions in a vortex core) or artificially implanted (such as nitrogen-vacancy centers in diamond), are then studied in concert with the delocalized collective driven-dissipative dynamics.This project will further our understanding of fundamental properties of correlated quantum materials on three fronts: (i) Through the prism of their novel transport properties based on topological conservation laws (which has so far eluded much attention in solid state); (ii) By tuning an ensemble of individually-accessible quantum bits into strong (electromagnetic) coupling with a topological material, and quantifying the induced entanglement; and (iii) Exploring these questions for a driven-dissipative dynamics, where the non-Hermitian character enriches both the topological properties and the associated quantum correlations. The project thus sets out to offer new general-purpose probes of dynamic properties of correlated materials, with an eye on topology, quantum entanglement, and dissipation, along with the interplay thereof.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.