Optimal control for preparing fractional quantum Hall states in optical lattices

TL;DR

This paper introduces optimal-control techniques to efficiently prepare fractional quantum Hall states in optical lattices, enabling larger and more complex topological states to be realized in quantum simulators.

Contribution

It develops optimized protocols based on recent experiments that accelerate the creation of FQH states and are robust against errors, facilitating scalable quantum simulations.

Findings

Optimal control significantly reduces preparation time.

Protocols are robust to control errors and disorder.

Methods are suitable for larger FQH states.

Abstract

Preparing fractional quantum Hall (FQH) states represents a key challenge for quantum simulators. While small Laughlin-type states have been realized by manipulating two atoms or two photons, scaling up these settings to larger ensembles stands as an impractical task using existing methods and protocols. In this work, we propose to use optimal-control methods to substantially accelerate the preparation of small Laughlin-type states, and demonstrate that the resulting protocols are also well suited to realize larger FQH states under realistic preparation times. Our schemes are specifically built on the recent optical-lattice experiment [Leonard et al., Nature (2023)], and consist in optimizing very few control parameters: the tunneling amplitudes and linear gradients along the two directions of the lattice. We demonstrate the robustness of our optimal-control schemes against control errors and disorder, and discuss their advantages over existing preparation methods. Our work paves the way to the efficient realization of strongly-correlated topological states in quantum-engineered systems.