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arXiv:2501.10720 · Physical review. B./Physical review. B

Optimal control for preparing fractional quantum Hall states in optical lattices

Ling-Na Wu, Xikun Li, Nathan Goldman, Botao Wang

Published Jun 3, 2025• 3 citations
arXivHTMLPDF

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 [L\'eonard et al., Nature (London) 619, 495 (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.

DOI
10.1103/physrevb.111.235111

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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 [L'eonard et al., Nature (London) 619, 495 (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.
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Fractional quantum Hall (FQH) states are a central paradigm of strongly correlated quantum matter and a key platform for topological quantum computation. Here, we propose a purely dissipative protocol based on local loss and pump channels for preparing Laughlin-like states at filling 1/31/31/3, with a possible extension to other 1/M1/M1/M filling states. We show that the Laughlin-like state is the exact unique steady state of the Lindbladian under open boundary conditions. Finite-size analysis of the Lindbladian gap suggests efficient dissipative preparation over the system sizes and parameter regime considered. We further demonstrate adiabatic pumping of a Laughlin-like state through slow modulation of the pump channels during the evolution. Our work opens a feasible route to preparing and manipulating FQH states on near-term quantum simulators.