Growing Extended Laughlin States in a Quantum Gas Microscope

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 ν=½-Laughlin state has been realized experimentally for a small system of two particles on 4×4 sites [Leonard et al., arXiv:2210.10919].

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 adiabatically connecting multiple copies of the already existing 4×4-system. First, we present a minimal setting obtained by coupling two of such patches, producing an extended 8×4-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 might give experimental access to the central charge, square-like geometries are advantageous for creating quasi-holes in view of braiding protocols.