Quantum simulation in Fock-state lattices

Fock-state lattices (FSLs) consist of the Fock states of photons and atoms, establishing a quantum photonic platform for simulating condensed matter physics. Remarkably, various topological phenomena, such as topological edge states, strain-induced Landau levels, the valley Hall effect, and the quantum anomalous Hall effect, are intricately linked to the quantum properties of light. Recent advancements in state-of-the-art superconducting circuits have enabled the observation of these topological quantum photonic phenomena. With scalable dimensions and flexible structure engineering, FSLs offer a novel tool for investigating high-dimensional topological physics and devising innovative devices for quantum information processing. This review delves into the latest theoretical and experimental developments in this emerging field, situated at the intersection of quantum optics, topological physics, and quantum information. {GRAPHIACAL ABSTRACT}