Growing Extended Laughlin States in a Quantum Gas Microscope: A Patchwork Construction

The study of fractional Chern insulators and their exotic anyonic excitations poses a major challenge in current experimental and theoretical research. Quantum simulators, in particular ultracold atoms in optical lattices, provide a promising platform to realize, manipulate, and understand such systems with a high degree of controllability. Recently, an atomic $\nu=1/2$ Laughlin state has been realized experimentally for a small system of two particles on 4 by 4 sites. The next challenge concerns the preparation of Laughlin states in extended systems, ultimately giving access to anyonic braiding statistics or gapless chiral edge-states in systems with open boundaries. Here, we propose and analyze an experimentally feasible scheme to grow larger Laughlin states by connecting multiple copies of the already existing 4-by-4-system. First, we present a minimal setting obtained by coupling two of such patches, producing an extended 8-by-4-system with four particles. Then, we analyze different preparation schemes, setting the focus on two shapes for the extended system, and discuss their respective advantages: While growing strip-like lattices could give experimental access to the central charge, square-like geometries are advantageous for creating quasi-hole excitations in view of braiding protocols. We highlight the robust quantization of the fractional quasi-hole charge upon using our preparation protocol. We benchmark the performance of our patchwork preparation scheme by comparing it to a protocol based on coupling one-dimensional chains. We find that the patchwork approach consistently gives higher target-state fidelities, especially for elongated systems. The results presented here pave the way towards near-term implementations of extended Laughlin states in quantum gas microscopes and the subsequent exploration of exotic properties of topologically ordered systems in experiments.