Strongly Correlated Quantum Systems: From Electronic Materials to Cold Atoms to Photons

技术概述：该奖项支持理论凝聚态物理和原子物理界面的理论研究和教育。物理学的进步来自理论和实验的相互促进。在超冷原子领域，关于费什巴赫共振、光学晶格和低维系统的理论思想导致了几种类型的强相关多体系统的实验实现。该领域的未来进展需要理论投入，以开发新的方法来创造、操纵、识别和表征用冷原子实现的物质的新量子态。本研究的目标之一是开发新的理论工具来研究强相关量子系统的相干动力学。了解相互作用的多体系统的非平衡动力学对于接触冷原子系综的实验至关重要。理论技术将包括微扰展开，有效场论分析，精确解的应用，点阵系统的数值方法。该项目将采用考虑特定系统的策略，目标是开发通用工具来研究相互作用的费米子和玻色子系统的动力学，并提出一个理解物质强相关状态的物理的通用框架。该项目的另一个目标是寻找新的方法来表征相互作用的多体系统的非平凡相关性，使用适合冷原子系综的实验技术。研究数据的新方法，如飞行时间实验的量子噪声分析和干涉实验中条纹可见性的分析将被强调。创建强相关系统的新方法的理论研究也是这个项目的重要组成部分。该项目将探索各种可能性，从光学晶格中的旋量凝聚物和极性分子的非平均场态到中空光纤中的光子唐克斯气体。后者的想法是创建一个一维光子系统，其中光学非线性非常大，以至于光子基本上成为不可穿透的粒子。这样的系统应该表现出光子“费米化”的特征，包括强光子反聚束和晶体样相关的出现。它应该为非线性量子光学和强相关电子系统之间提供一个新的有趣的接口。该项目的另一个组成部分是利用各种实验技术的最新进展，探索研究固体中电子强相关态的新方法，包括共振软x射线散射、双光电发射光谱和高分辨率扫描隧道显微镜。培养学生和博士后研究人员是这个项目的重要组成部分。学生和博士后积极参与PI的研究，并接触到物理学多个领域的广泛问题。非技术概述：该奖项支持理论凝聚态物理和原子物理界面的理论研究和教育。这个研究项目的重点是在被光捕获的原子系统中出现的物质的新状态，以及在复杂材料中的低能电子。在这些系统和材料中，原子或电子彼此之间强烈的相互作用导致物质的新状态的出现，这些状态具有有趣的特性，经常显示出根本的新现象。先进的理论研究工具将被用来理解可能的物质新状态，并提出新的方法来实验探测这些系统，并操纵它们的量子力学状态，从而识别物质的新状态并发现它们的微妙本质。对被困在周期性光晶格中的冷原子的研究，提供了探索强相互作用系统的可能性，而这是电子在材料中不可能实现的。对一个领域的理解的进步会推动另一个领域的进步。物质新状态的不寻常特性，无论它们是如何表现出来的，以及与之相关的不寻常现象，与我们宇宙的任何其他方面一样，都具有根本的兴趣和重要性。了解如何操纵新发现的物质的量子力学状态，为执行计算和新设备技术提供了强大的新方法，这将有助于保持美国的竞争力。培养学生和博士后研究人员是这个项目的重要组成部分。学生和博士后积极参与研究，并接触到物理学几个领域的广泛问题。这个项目有助于培养高素质的受过科学训练的下一代劳动力。

TECHNICAL SUMMARY:This award supports theoretical research and education at the interface of theoretical condensed matter physics and atomic physics. Advances in physics come from mutual stimulation of theory and experiments. In the field of ultracold atoms theoretical ideas about Feshbach resonances, optical lattices, and low dimensional systems lead to experimental realization of several types of strongly correlated many body systems. Future progress in the field requires theoretical input into developing new methods for creation, manipulation, identification, and characterization of novel quantum states of matter realized with cold atoms. One of the goals of this research is to develop new theoretical tools for studying coherent dynamics of strongly correlated quantum systems. Understanding non-equilibrium dynamics of interacting many-body systems is crucial for making contact with experiments on ensembles of cold atoms. Theoretical techniques will include perturbative expansions, analysis of effective field theories, application of exact solutions, numerical methods for lattice systems. This project will adopt a strategy of considering particular systems with a goal of developing general tools for studying dynamics of interacting fermionic and bosonic systems and bringing out a common framework for understanding the physics of strongly correlated states of matter. Another goal of this project is to find new ways of characterizing non-trivial correlations of interacting many body systems using experimental techniques appropriate for cold atoms ensembles. Novel approaches to examining the data, such as quantum noise analysis of the time of flight experiments and analysis of fringe visibility in interference experiments will be emphasized. The theoretical investigation of new methods for creating strongly correlated systems is also an essential part of this project. This project will explore a variety of possibilities starting from non mean field states of spinor condensates and polar molecules in optical lattices to a Tonks gas of photons in a hollow optical fiber. The idea of the latter is to create a one dimensional system of photons where optical non-linearity is so large that photons become essentially impenetrable particles. Such a system should exhibit features of photon "fermionization" including the appearance of strong photon antibunching and crystal like correlations. It should provide a new intriguing interface between nonlinear quantum optics and strongly correlated electron systems. Another component of this project involves exploring new methods for studying strongly correlated states of electrons in solids using recent progress in a variety of experimental techniques, including resonant soft x-ray scattering, double photoemission spectroscopy, and high resolution scanning tunneling microscopy.Training students and postdoctoral researchers is a vital component of this project. Students and postdocs are actively involved in the research of the PI and are exposed to a wide range of problems in several areas of physics. NON-TECHNICAL SUMMARY:This award supports theoretical research and education at the interface of theoretical condensed matter physics and atomic physics. This research project focuses on new states of matter that arise in systems of atoms trapped by light, and in low-energy electrons in complex materials. In these systems and materials, the atoms or the electrons interact strongly with each other resulting in the emergence of new states of matter with intriguing properties that often display fundamentally new phenomena. Advanced tools of theoretical research will be brought to bear to understand possible new states of matter and propose new ways to experimentally probe these systems and to manipulate their quantum mechanical states so as to identify new states of matter and discover their subtle nature. The study of cold atoms trapped in periodic lattices of light offer the possibility to explore strongly interacting systems in ways that are not possible for electrons in materials. Advances in understanding one area enable advances in the other. The unusual properties of new states of matter however they are manifest and the unusual phenomena associated with them are of no less fundamental interest and importance than any other aspect of our universe. Understanding how to manipulate newly discovered quantum mechanical states of matter offers the possibility of powerful new ways to perform computation and new device technologies that will help keep America competitive. Training students and postdoctoral researchers is a vital component of this project. Students and postdocs are actively involved in the research and are exposed to a wide range of problems in several areas of physics. This project contributes to the high caliber scientifically trained workforce of the next generation.