Strongly Interacting Atoms under Quantum Gas Microscope

理解由许多强相互作用的量子单元组成的量子物质，如原子，自旋或量子比特，仍然是一个巨大的挑战。它支撑着我们设计更好的材料或解决经典计算机无法解决的难题的能力。量子模拟器是一个人造系统，其中各个量子单元及其耦合都处于精确控制之下。量子气体的超冷原子被限制在由激光形成的光学晶格中，已经成为量子模拟的领先平台。最近发明的量子气体显微镜提供了前所未有的精确读出这些模拟器与单原子和单网站的分辨率。它开辟了新的机会，以探测强相互作用的超冷原子的性质限制在两个维度，以解决长期悬而未决的问题，在强相关的量子物质，例如关于d波超流体的存在费米-哈伯德模型或量子自旋液体在挫折自旋模型。目前正在进行的实验需要从理论上定量准确的预测，以提高超流体的转变温度或侦察出的自旋液体在参数空间中的位置。这些任务是具有挑战性的，因为强相互作用的量子气体与许多密切竞争的订单受损。为了平等对待它们，人们通常限于小系统尺寸或低动量分辨率，以保持计算易于处理。 拟议的研究刺激了量子气体，量子模拟和机器学习之间的交叉施肥。本项目将培养学生掌握高性能计算和数据分析的可转移技能。本项目开发新的高精度数值算法，用于计算二维晶格中强相互作用超冷原子的性质。提出了两种创新的多体技术来克服上述技术挑战。首先，我们将发展具有全动量分辨率的泛函重整化群，以精确地追踪光晶格上相互作用费米子原子的竞争多体不稳定性。它将被应用于优化光学晶格设计，以促进排斥费米-哈伯德气体中的d波超流性。其次，通过机器学习的启发，多体波函数的神经网络参数化，解决了光晶格中冷原子的受抑量子自旋模型。将开发基于前馈神经网络的变分分析方法，以解决其基态的性质。所提出的工作扩展了强相互作用原子和自旋的精确多体算法的边界。它通过在图形处理器上大规模并行求解流方程，将泛函重整化群中运行的耦合数从数十万提高到数千万。由此产生的上级分辨率将产生更准确的相边界和转变温度的估计，以指导实验。大规模神经网络模拟将有助于回答关于量子自旋系统中自旋液体和其他奇异相的存在和性质的开放性问题。这些开发的多体技术是通用的，可以应用于相关的量子材料或相互作用的分子和捕获离子的量子自旋模型。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

Comprehending quantum matter consisting of many strongly interacting quantum units, such as atoms, spins, or quantum bits, remains a great challenge. It underpins our capacity to design better materials or to solve hard problems beyond the reach of classical computers. A quantum simulator is a man-made system where the individual quantum units as well as their couplings are under precise control. Quantum gases of ultracold atoms confined in optical lattices formed by laser light have emerged as a leading platform for quantum simulation. The recent invention of the quantum gas microscope offers unprecedented precision readout of these simulators with single-atom and single-site resolution. It opens up new opportunities to probe the properties of strongly interacting ultracold atoms confined in two dimensions to solve long-standing open problems in strongly correlated quantum matter, for instance regarding the existence of d-wave superfluid in the Fermi-Hubbard model or quantum spin liquids in frustrated spin models. The ongoing experiments demand from theory quantitatively accurate predictions to boost the superfluid transition temperature or to scout out the locations of spin liquids in the parameter space. These tasks are challenging because strongly interacting quantum gases are marred with many closely competing orders. To treat them on equal footing, one is usually limited to small system sizes or low momentum resolution in order to keep the calculation tractable. The proposed research stimulates the cross-fertilization between quantum gases, quantum simulation and machine learning. Students involved in this project will be trained to acquire transferable skills in high performance computing and data analysis.This project develops new high-precision numerical algorithms to compute the properties of strongly interacting ultracold atoms confined in two-dimensional lattices. Two innovative many-body techniques are proposed to overcome the aforementioned technical challenges. First, functional renormalization group with full momentum resolution will be developed to accurately track the competing many-body instabilities for interacting fermionic atoms on optical lattices. It will be applied to optimize the optical lattice designs to promote d-wave superfluidity in repulsive Fermi-Hubbard gases. Second, frustrated quantum spin models of cold atoms localized in optical lattices are solved by neural network parametrization of the many-body wave function inspired by machine learning. Variational ansatz based on feed-forward neural networks will be developed to resolve the nature of their ground states. The proposed work expands the boundary of precision many-body algorithms for strongly interacting atoms and spins. It improves the number of running couplings in functional renormalization group from hundred thousands to tens of millions by solving the flow equations massively parallel on Graphics Processing Units. The resultant superior resolution will yield more accurate phase boundaries and estimations of the transition temperature to guide experiments. Large-scale neural network ansatz will help answer open questions regarding the existence and nature of spin liquids and other exotic phases in quantum spin systems. These many-body techniques developed are general and can be applied to correlated quantum materials or quantum spin models of interacting molecules and trapped ions.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.