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Measuring Nonlocal Brane Order with Error-Corrected Quantum Gas Microscopes

Junhyeok Hur1,*, Wonjun Lee2,3,*, Kiryang Kwon1, SeungJung Huh1, Gil Young Cho2,3,4,†, and Jae-yoon Choi1,‡

  • 1Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea
  • 2Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Republic of Korea
  • 3Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang 37673, Republic of Korea
  • 4Asia-Pacific Center for Theoretical Physics, Pohang, 37673, Republic of Korea

  • *These authors contributed equally to this work.
  • †gilyoungcho@postech.ac.kr
  • ‡jaeyoon.choi@kaist.ac.kr
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Phys. Rev. X 14, 011003 – Published 8 January, 2024

DOI: https://doi.org/10.1103/PhysRevX.14.011003

Abstract

Exotic quantum many-body states, such as Haldane and spin liquid phases, can exhibit remarkable features like fractional excitations and non-Abelian statistics and offer new understandings of quantum entanglement in many-body quantum systems. These phases are classified by nonlocal correlators that can be directly measured in atomic analog quantum simulating platforms, such as optical lattices and Rydberg atom arrays. However, characterizing these phases in large systems is experimentally challenging because they are sensitive to local errors like atom loss, which suppress its signals exponentially. Additionally, protocols for systematically identifying and mitigating uncorrelated errors in analog quantum simulators are lacking. Here, we address these challenges by developing an error-correction method for large-scale neutral atom quantum simulators using optical lattices. Our error-correction method can distinguish correlated particle-hole pairs from uncorrelated holes in the Mott insulator. After removing the uncorrelated errors, we observe a dramatic improvement in the nonlocal parity correlator and find the perimeter scaling law. Furthermore, the error model provides a statistical estimation of fluctuations in site occupation, from which we measure the generalized brane correlator and confirm that it can be an order parameter for Mott insulators in two dimensions. Our work provides a promising avenue for investigating and characterizing exotic phases of matters in large-scale quantum simulators.

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Popular Summary

Topological order in quantum many-body systems has drawn significant attention due to its potential applications in scalable fault-tolerant quantum computations. However, its practical use is still limited to small systems because of vulnerabilities to local errors, such as atom loss in atomic analog quantum simulators that use either an optical lattice or a tweezer atom array. Here, for the first time, we develop an error-correction method for atomic quantum simulators and measure nonlocal order parameters in topological 2D Mott insulators.

In the Mott insulator, the average occupation of each lattice site is an integer but exhibits atom number fluctuations due to the formation of entangled particle-hole pairs. These fluctuations can be measured with a “generalized brane correlator,” a recently proposed 2D order parameter that signals the superfluid-to-Mott insulator quantum phase transition.

In our experiment with a neutral atom array, however, the nonlocal 2D order is suppressed due to the random appearance of uncorrelated holes (errors), which arise because of the system’s finite temperature and detection losses. In this work, we develop an error-correction method that removes the uncorrelated holes. Using this method, we measure the generalized brane correlators across the quantum phase transition and confirm that the transition curve is independent of the domain size.

This work opens a new avenue to observe and characterize topological phases in higher dimensions in noisy quantum simulation platforms.

Article Text

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Phys. Rev. X 14, 011003– Published 8 January, 2024
  • Received 16 May 2023
  • Accepted 15 November 2023
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