Competing Orders in Quantum Gases with Long-range Interactions

最近对磁性原子和/或极性分子(具有电偶极矩的分子)捕获的系综的实验已经达到了极低的温度，在这种温度下量子力学效应比比皆是。极性原子和分子各向异性地相互吸引和/或排斥(就像一对磁铁)，捕获的此类粒子的集合预计会显示出各种集体现象，这是目前许多研究的重点。现代对偶极气体的实验正试图提供一个受控的环境，在其中合成、调整和发现极性量子物质的新相，以补充在更高温度下常见的固体、液体、气体和等离子体相。虽然极地系统有望显示出各种各样的新现象，但它们还没有被很好地理解，它们的性质在理论上是具有挑战性的。困难来自于它们的敏感性：即使是密度或温度的微小变化也会改变系综相，从而极大地改变观测到的性质。该项目正在开发新的理论工具，用于分析超冷偶极物质的多个相，以提高我们对最近的实验观测的理解。除了物理，研究生和本科生还将通过这个项目接受科学计算、数据分析和可视化方面的培训。该项目将为具有远程相互作用的量子气体开发两种创新的多体技术。第一个是有限温度下连续态费米气体的泛函重整化群。它将用于分析二维费米偶极气体的多体不稳定性和相图。第二种是对位于深光学晶格中的偶极原子或分子的张量网络变分。它将被作为基准，并进行调整，以解决具有竞争和长期交换相互作用的有效自旋模型。重整化群技术还将用于研究其他量子气体系统的多体相，包括Rydberg修饰的费米气体和自旋-轨道耦合的费米气体。

Recent experiments with trapped ensembles of magnetic atoms and/or polar molecules (molecules that have an electric dipole moment) have achieved the extremely cold temperatures at which quantum mechanical effects abound. Polar atoms and molecules attract and/or repel one another anisotropically (like a pair of magnets), and trapped collections of such particles are expected to display a variety of collective phenomena that are the focus of much current research. Modern experiments with dipolar gases are attempting to provide a controlled environment in which to synthesize, tune, and discover novel phases of polar quantum matter, complementary to the solid, liquid, gas and plasma phases familiar at higher temperatures. While polar systems are expected to display a wide variety of new phenomena, they are not yet well understood and their properties are challenging to predict theoretically. The difficulty arises from their sensitivity: Even small changes in density or temperature can change the phase of the ensemble, and so change observed properties dramatically. This project is developing new theoretical tools for the analysis of the plurality of phases of ultracold dipolar matter in order to improve our understanding of recent experimental observations. Graduate and undergraduate students will be trained through this project in scientific computing, data analysis and visualization in addition to physics. The project will develop two innovative many-body techniques for quantum gases with long-range interactions. The first is functional renormalization group for continuum Fermi gases at finite temperatures. It will be used to analyze the many-body instabilities and phase diagrams of dipolar Fermi gases in two-dimensions. The second is tensor network variational ansatz for dipolar atoms or molecules localized in deep optical lattices. It will be benchmarked and adapted to solve effective spin models with competing and long-range exchange interactions. The renormalization group technique will also be applied to study the many-body phases of other quantum gas systems including Rydberg dressed Fermi gases and spin-orbit coupled Fermi gases.