Strongly Interacting Atoms under Quantum Gas Microscope

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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.