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

TL;DR

This paper proposes a feasible method to grow larger Laughlin states in ultracold atom systems by connecting smaller patches, enabling experimental exploration of topological properties and anyonic excitations.

Contribution

It introduces a patchwork construction scheme for extending Laughlin states in quantum gas microscopes, improving state fidelity over previous methods.

Findings

Patchwork scheme achieves higher fidelity in state preparation.

Robust quantization of fractional quasi-hole charge demonstrated.

Extended systems enable exploration of topological properties.

Abstract

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.