CAREER: Quantum Gas Microscopy of Frustrated Hubbard Systems

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General audience abstract:Quantum systems of many electrons are computationally intractable but are of profound importance for the understanding of material properties like superconductivity and quantum magnetism. Direct imaging of electrons in materials including their local correlations and entanglement is almost impossible, but quantum simulation can shed light on the microscopic properties of these complex quantum systems. This CAREER award supports quantum simulation of these systems using fermionic atoms cooled to a few billionth of a degree trapped in an artificial crystal of light. This approach provides a versatile platform with wide tunability based on well-characterized components. A quantum gas microscope with high-resolution imaging capabilities will be constructed and used to study many-fermion systems with single-site and single-atom resolution in geometrically frustrated lattices. In these frustrated systems, several energetic constraints cannot be minimized at the same time, and their competition leads to exotic low-temperature properties. This research effort will investigate the impact of the lattice geometry on the properties of many-fermion systems and will provide insights guiding the search for novel high-temperature superconductors. The research activities are embedded in a science education program operating at the K-12, undergraduate, graduate, and postdoctoral level. The two main pillars of the educational and outreach program are (a) a hands-on workshop program for K-12 students and (b) a mobile exhibition of active-learning experiments for the general public.Technical audience abstract:Geometric frustration in quantum many-body systems leads to intriguing phenomena like exotic emergent low-energy physics, massive ground-state entanglement, and topological order. It is naturally realized in systems with antiferromagnetic interactions on non-bipartite lattices where antiparallel orientation between all neighboring spins is inhibited. This research program will realize the Fermi-Hubbard model on a triangular lattice as a manifestation of a non-bipartite lattice system with antiferromagnetic interactions. Ultracold fermionic lithium atoms will be loaded in a triangular optical lattice and detected using the state-of-the-art techniques of quantum gas microscopy to resolve all individual atoms in the lattice, allowing unprecedented access to single-atom observables and real-space correlations. All Hamiltonian parameters can be adjusted over a wide range and calibrated independently, enabling an extensive study of the phase diagram. The absence of a unique ground state leads to a rich phase diagram and may allow for the realization of a stable quantum spin liquid in a Fermi-Hubbard model as predicted by numerical calculations. The main research thrusts are: (a) Probing the phase diagram of geometrically frustrated Fermi lattice gases. (b) Detecting short-range correlations. (c) Measuring chiral correlations in the triangular Hubbard model. (d) Searching signatures of a quantum spin liquid.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.