Measuring the Chern-Simons invariant in quantum gases
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915483122401280 |
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| author | Yi, Chang-Rui Yu, Jinlong Yuan, Huan Chen, Xin Guo, Jia-Yu Zhang, Jinyi Chen, Shuai Pan, Jian-Wei |
| author_facet | Yi, Chang-Rui Yu, Jinlong Yuan, Huan Chen, Xin Guo, Jia-Yu Zhang, Jinyi Chen, Shuai Pan, Jian-Wei |
| contents | Chern-Simons (CS) invariant is a fundamental topological invariant describing the topological invariance of 3D space based on the Chern-Simons field theory. To date, direct measurement of the CS invariant in a physical system remains elusive. %to be 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 quasi-momentum 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 $\pm 1$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measuring the Chern-Simons invariant in quantum gases Yi, Chang-Rui Yu, Jinlong Yuan, Huan Chen, Xin Guo, Jia-Yu Zhang, Jinyi Chen, Shuai Pan, Jian-Wei Quantum Gases Atomic Physics Chern-Simons (CS) invariant is a fundamental topological invariant describing the topological invariance of 3D space based on the Chern-Simons field theory. To date, direct measurement of the CS invariant in a physical system remains elusive. %to be 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 quasi-momentum 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 $\pm 1$ 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. |
| title | Measuring the Chern-Simons invariant in quantum gases |
| topic | Quantum Gases Atomic Physics |
| url | https://arxiv.org/abs/2509.05774 |