CAREER: Entanglement, Pairing and Superfluidity at the Interface between Atomic and Nuclear Physics.

物理学的许多领域正在进入信息时代，计算处于研究的前沿。这个新时代的关键概念之一是纠缠的量子力学性质，它描述了量子粒子如何纯粹由于其量子力学性质而相互关联。粒子间相互作用对纠缠的影响是一个具有挑战性的问题，因为相互作用（特别是强相互作用）驱动相变，并负责物质的有趣性质。与信息相关的量，如纠缠熵，在量子相变中起着至关重要的作用，并且是量子计算和黑洞等看似不同领域的核心。PI将利用原子、核和凝聚态物理的计算进展，在这些领域之间的界面上对强相互作用的超流体系统进行更深入的了解，在这些领域中，纠缠特性在很大程度上仍未被探索。该项目将提供对各种系统的纠缠及其与热力学可观测值的相关性的精确预测。研究生和本科生将参与多个层面，重点是正在进行的课程和与北卡罗来纳大学彭布罗克分校的轨道开发合作。该项目旨在精确描述与原子、分子和核物理相关的一系列强耦合、非相对论性、少费米子和多费米子系统。这里考虑的系统将包括多个空间维度、自由空间、谐波陷阱和弱到强相互作用的制度。热力学性质（静态、动态、结构和配对相关性）及其与纠缠（纠缠熵、互信息）的联系将使用非摄动方法确定，包括数值点阵场论方法以及半解析展开（例如维数和算子积展开）。为此，将实施先进的计算方法和算法，并探索计算纠缠熵的新方法。方法（代码、脚本、技术说明）和数据（从辅助现场配置到物理结果）将在网上提供。

Many areas in physics are entering an information age, with computation at the forefront of research. One of the key notions in this new era is the quantum-mechanical property of entanglement, which characterizes how quantum particles are correlated with each other purely as a result of their quantum-mechanical nature. The influence of inter-particle interactions on entanglement is a challenging question, as interactions (in particular strong ones) drive phase transitions and are responsible for intriguing properties of matter. Information-related quantities, such as the entanglement entropy, play an essential role in quantum phase transitions and are central to seemingly disparate areas, such as quantum computation and black holes. The PI will leverage computational progress in atomic, nuclear and condensed matter physics to pursue a deeper understanding of strongly interacting superfluid systems at the interface between those areas, where entanglement properties remain largely unexplored. This project will provide precise predictions of entanglement and its correlation with thermodynamic observables across a wide variety of systems. Graduate and undergraduate students will be engaged at multiple levels, with emphasis on an ongoing curriculum and track-developing collaboration with the University of North Carolina at Pembroke.This project aims for a precise characterization of a wide range of strongly coupled, non-relativistic, few- and many-fermion systems of relevance to atomic, molecular, and nuclear physics. The systems considered here will include multiple spatial dimensions, free space, harmonic traps, and weakly to strongly interacting regimes. Thermodynamic properties (static, dynamic, structural, and pairing correlations) and their connection to entanglement (entanglement entropies, mutual information) will be determined using non-perturbative approaches, including numerical lattice field theory methods as well as semi-analytic expansions (e.g. the virial and operator-product expansions). To this end, advanced computational methods and algorithms will be implemented and new approaches will be explored to calculate entanglement entropies. The methods (codes, scripts, technical notes) and the data (from auxiliary field configurations to the physical results) will be made available online.