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  • Featured in Physics
  • Open Access

Topological Order in Symmetric Blockade Structures

Tobias F. Maier, Hans Peter Büchler, and Nicolai Lang*

  • *Contact author: nicolai.lang@itp3.uni-stuttgart.de
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PRX Quantum 6, 030340 – Published 2 September, 2025

DOI: https://doi.org/10.1103/dtlf-2q82

Abstract

The bottom-up design of strongly interacting quantum materials with prescribed ground-state properties is a highly nontrivial task, especially if only simple constituents with realistic two-body interactions are available on the microscopic level. Here we study two- and three-dimensional structures of two-level systems that interact via a simple blockade potential in the presence of a coherent coupling between the two states. For such strongly interacting quantum many-body systems, we introduce the concept of blockade graph automorphisms to construct symmetric blockade structures with strong quantum fluctuations that lead to equal-weight superpositions of tailored states. Drawing from these results, we design a quasi-two-dimensional periodic quantum system that—as we show rigorously—features a topological Z2 spin liquid as its ground state. Our construction is based on the implementation of a local symmetry on the microscopic level in a system with only two-body interactions.

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synopsis

Quantum Materials Built from Scratch

Published 2 September, 2025

A proposed method could help scientists coax simple atomic systems into quantum states that have useful, tailored properties.

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Popular Summary

Some experimental platforms (like arrays of atoms) facilitate the placement and coherent control of hundreds of elementary quantum systems that interact via simple two-body interactions. This opens the possibility of engineering quantum materials from scratch and motivates the “inverse problem” of quantum many-body physics: given a “toolbox” of microscopic constituents (like atoms) that can be placed freely and controlled precisely and that interact only via two-body interactions, is it possible to robustly engineer a prescribed quantum phase of matter—and if so, how—?

Here we study this question for a toolbox that comprises elementary two-level systems (say atoms) that interact via a blockade mechanism: atoms separated by less than a given distance cannot be excited simultaneously. We assume that quantum fluctuations are induced by a uniform, coherent coupling between the two levels of the atoms.

Despite the simplicity of this toolbox, we systematically show how to engineer a many-body system that realizes the famous toric code topological order, a highly entangled quantum phase with potential applications for quantum computing. To do so, we introduce a particular type of symmetry that enforces strong quantum fluctuations and makes the ground state an equal-weight superposition of “loop configurations” of excitations. We then rigorously prove that this ground state has the sought-after topological order. This construction is interesting because it realizes an elusive quantum phase using only experimentally accessible two-body interactions.

In a broader sense, our results show how to incorporate quantum fluctuations systematically into the design process of artificial quantum materials.

Article Text

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PRX Quantum 6, 030340– Published 2 September, 2025
  • Received 21 March 2025
  • Revised 8 June 2025
  • Accepted 7 July 2025
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