RUI New Generation of AI-Augmented Quantum Monte Carlo Libraries to Guide the Search for Exotic Superfluid Phases in Cold Atoms

该项目将把成熟的最先进的数值技术与创新的人工智能工具结合起来，计算强相关费米超流体的平衡和动力学性质。在非常活跃的超冷原子领域，该项目的结果将指导对奇异超流体相的实验研究，例如依赖于非常规配对机制的物质的非平凡超流体状态或迷人的拓扑超流体的存在。该项目的新见解可能会对物理学产生深远的影响，甚至超越冷原子领域，并可能为更深入地了解非常规超导体和核物质中的超流状态铺平道路。将开发新的数据分析工具和可视化技术，以捕捉最重要的物理机制。PI计划投入大量的努力，使尽可能多的人可以使用这些方法和主题，并解决教授量子力学的新方法。学生将能够运行虚拟实验，探索物质的新阶段，并将有一个独特的机会来学习如何成为未来的科学家。新一代的量子场量子蒙特卡罗技术将被提出：人工智能工具将指导一个自洽的过程，以尽量减少由于近似的偏见。这将通过在从量子蒙特卡罗数据学习的反馈过程中优化试验波函数来实现。该项目有望为费米超流体提供准确的非微扰数据。该研究将解决平衡性质，如配对，密度和自旋相关性，以及动力学性质，如光谱函数和动力学结构因子，这些性质可以获得系统的低能激发。准确的数值数据将提供指导的实验中的主要挑战，检测新的奇异相位在冷原子，特别是专注于复杂的纠缠秩序的自旋极化系统时，自旋轨道耦合存在。在对这种超流体相的物理机制的基本理解方面也有望取得实质性进展。将讨论自旋极化系统中具有有限动量的库珀对的形成，将研究与密度和自旋序的相互作用，并研究自旋轨道耦合的作用，以及观察非平凡拓扑性质的可能性。通过计算动力学相关性来研究系统激发态的流形，将使PI能够直接将预测与光谱和散射实验进行比较，并计算集体模式的色散，这对于奇异相的实验检测至关重要。除了指导实验研究外，这些结果还将作为强相关系统的多体理论和计算方法的有价值的基准，在这些系统中，简单的微扰方法注定会失败。最后，PI计划致力于开发新的可视化工具来捕捉关键的物理机制，预计将为培养下一代学生，教师和研究人员创造最佳环境。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值进行评估，更广泛的影响审查标准。

This project will interface well-established state-of-the-art numerical techniques with innovative artificial intelligence tools to compute equilibrium and dynamical properties of strongly correlated Fermi superfluids. In the very active field of ultracold atoms, the results of this project will guide experimental searches for exotic superfluid phases, such as non-trivial superfluid states of matter that rely on unconventional pairing mechanisms or the existence of fascinating topological superfluids. The new insights that will come from this project may have a deep impact in physics, even beyond the field of cold atoms, and may pave the way for a deeper understanding of superfluid states in unconventional superconductors and in nuclear matter. Novel data analysis tools and visualization techniques will be developed to capture the most important physical mechanisms. The PI plans to dedicate substantial effort to make the methods and topics accessible to as many people as possible, and to address novel ways to teach quantum mechanics. Students will be able to run virtual experiments and to explore new phases of matter and will have a unique opportunity to learn how to become the scientists of the future.A new generation of auxiliary-field quantum Monte Carlo techniques will be proposed: artificial intelligence tools will guide a self-consistent procedure to minimize the bias due to the approximations underlying the technique. This will be achieved through the optimization of the trial wave function within a feedback process which learns from the quantum Monte Carlo data. This project is expected to generate accurate non-perturbative data for Fermi superfluids. The study will address both equilibrium properties, like pairing, density and spin correlations, and dynamical properties, like spectral functions and dynamical structure factors, which give access to the low-energy excitations of the systems. The accurate numerical data will provide guidance to the experiments in the major challenge of detecting new exotic phases in cold atoms, with particular focus on complex intertwined orders in spin-polarized systems when spin-orbit coupling is present. Substantial advances in the fundamental understanding of the physical mechanisms underlying such superfluid phases are also expected. The formation of Cooper pairs with finite momentum in spin-polarized systems will be addressed, the interplay with density and spin order will be studied and the role of spin-orbit coupling will be investigated, in connection with the possibility of observing non-trivial topological properties. The study of the manifold of excited states of a system through the calculation of dynamical correlations will allow the PI to directly compare the predictions with spectroscopy and scattering experiments and to compute the dispersion of collective modes, which is crucial for the experimental detection of exotic phases. In addition to guiding experimental searches, the results will also serve as valuable benchmarks for many-body theories and computational methods for strongly correlated systems, where simple perturbative approaches are doomed to fail. Finally, the efforts that the PI plans to dedicate to the development of novel visualization tools to capture the key physical mechanisms are expected to create the best environment to train the next generation of students, teachers and researchers in quantum mechanics, starting from their undergraduate studies.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.