CAREER: New Algorithms to Simulate Ultracold Matter Out of Equilibrium and Redefine the Low-Temperature Frontier

理解和控制量子系统的动力学是世纪科学面临的基本挑战。不处于平衡状态的系统显示出“打破了支配平衡状态的规则”的现象。这种现象本质上是有趣的，并有潜在的应用价值。已经冷却到纳开尔文温度的气体为非平衡系统的研究提供了一个令人兴奋的新平台。超冷气体的实验使用光学提供的独特而精确的工具灵活地操纵和成像物质。虽然这些实验正在迅速推进，但也需要新的理论技术来帮助研究。 该项目将开发数值算法来解决一系列以前难以解决的实验重要问题。新算法将用于设计实验方案，将超冷物质冷却到更低的温度（该领域的巨大挑战），从而重新定义低温前沿。这将实现长期寻求和以前无法实现的物质相，包括模拟高温超导性的相。该项目将培训研究生、本科生和高中生使用新算法，促进其未来在非平衡物理学其他领域的应用。此外，还将编制可供公众使用的教育材料，统一物理学家经常使用的非平衡动力学概念，但在典型的物理课程中，即使有，也只是不明确地教授这些概念。这些课程将包括视频，阅读和练习，可用于自学或在课堂上，并将包括多个版本，每个版本为不同专业水平的学生设计，从非物理学家到实践研究人员。该项目将开发两种算法，动态数值关联簇扩展（NLCE）和簇截断维格纳近似（cl-TWA），其潜在地可以在膝上型计算机上在几分钟内精确地计算重要的超冷动力学，用于当前甚至最大的超级计算机也无法访问的情况。该算法通过识别和利用许多超冷动力学实验所依赖的特殊物理结构来实现其准确性。该项目将专注于应用这些新算法来设计和优化冷却超冷物质的新协议，这些协议分为三类：熵管理，绝热准备和工程耗散。该奖项反映了NSF的法定使命，通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Understanding and controlling the dynamics of quantum systems which are out of equilibrium is a fundamental challenge for science in the 21st century. Systems which are not in equilibrium display phenomena that "break the rules" that govern equilibrium phases. Such phenomena are intrinsically interesting and potentially useful for applications. Gases that have been cooled to nano-Kelvin temperatures provide an exciting new platform for the study of non-equilibrium systems. Experiments with ultracold gases flexibly manipulate and image matter using unique and precise tools provided by optics. While such experiments are rapidly advancing, new theoretical techniques are also needed to aid the investigations. This project will develop numerical algorithms to solve a range of previously intractable, experimentally important problems. The new algorithms will be used to design experimental schemes to cool ultracold matter to even lower temperatures (a grand challenge of the field), thereby redefining the low-temperature frontier. This would realize long-sought and previously inaccessible phases of matter, including phases which simulate high-temperature superconductivity. The project will train graduate, undergraduate, and high school students in the use of the new algorithms, facilitating their future use in other areas of non-equilibrium physics. In addition, publicly accessible educational materials will be developed which unify concepts in non-equilibrium dynamics that are used regularly by physicists, but which are taught only inexplicitly, if at all, in typical physics curricula. These lessons will include videos, reading, and exercises that can be used for self-study or in a classroom, and will include multiple versions, each designed for students of different levels of expertise, from non-physicists to practicing researchers.This project will develop two algorithms, a dynamical numerical linked cluster expansion (NLCE) and a cluster truncated Wigner approximation (cl-TWA), which potentially can accurately calculate important ultracold dynamics in minutes on a laptop for cases that are currently inaccessible to even the largest supercomputers. The algorithms achieve their accuracy by recognizing and exploiting special physical structures that underlie many ultracold dynamics experiments. The project will focus on applying these new algorithms to design and optimize new protocols for cooling ultracold matter that fall into three categories: entropy management, adiabatic preparation, and engineered dissipation. It will also partner with experiments to address fundamental questions of nonequilibrium physics, selected to align the strengths of the algorithms with emerging experimental directions.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.