Measuring the Chern-Simons invariant in quantum gases
The Chern-Simons (CS) invariant is a fundamental topological invariant describing the topological invariance of three-dimensional (3D) space based on the Chern-Simons field theory. To date, direct measurement of the CS invariant in a physical system remains elusive. Here, the CS invariant is experim...
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| Main Authors: | , , , , , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
28 August, 2025
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| In: |
Physical review
Year: 2025, Volume: 112, Issue: 2, Pages: 1-5 |
| ISSN: | 2469-9934 |
| DOI: | 10.1103/7wkb-lxg9 |
| Online Access: | Resolving-System, lizenzpflichtig, Volltext: https://doi.org/10.1103/7wkb-lxg9 Verlag, lizenzpflichtig, Volltext: https://link.aps.org/doi/10.1103/7wkb-lxg9 
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| Author Notes: | Chang-Rui Yi, Jinlong Yu, Huan Yuan, Xin Chen, Jia-Yu Guo, Jinyi Zhang, Shuai Chen, and Jian-Wei Pan |
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| 520 | |a The Chern-Simons (CS) invariant is a fundamental topological invariant describing the topological invariance of three-dimensional (3D) space based on the Chern-Simons field theory. To date, direct measurement of the CS invariant in a physical system remains elusive. Here, the CS invariant is experimentally measured by quenching a 2D optical Raman lattice with 1/2 spin in ultracold atoms. With a recently developed Bloch state tomography, we measure the expectation values of three Pauli matrices in 2D quasimomentum space plus 1D time [(2+1)D], and then respectively extract the Berry curvature and the corresponding Berry connection. By integrating the product of these two quantities, we obtain the CS invariants near ±1 and 0, which are consistent with theoretical predictions. We also observe transitions among these values, which indicates the change of the topology of the quantum state in (2+1)D quantum dynamics. | ||
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