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Observation of Topological Links Associated with Hopf Insulators in a Solid-State Quantum Simulator |
| X.-X. Yuan1†, L. He1†, S.-T. Wang1,2†, D.-L. Deng1,2,3, F. Wang1, W.-Q. Lian1, X. Wang1, C.-H. Zhang1, H.-L. Zhang1, X.-Y. Chang1, L.-M. Duan1,2* |
1Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084
2Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
3Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742-4111, USA
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X.-X. Yuan, L. He, S.-T. Wang et al 2017 Chin. Phys. Lett. 34 060302 |
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Abstract Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory and topological phases of matter, which distinguishes them from other classes of topological insulators. Here, we implement a model Hamiltonian for Hopf insulators in a solid-state quantum simulator and report the first experimental observation of their topological properties, including nontrivial topological links associated with the Hopf fibration and the integer-valued topological invariant obtained from a direct tomographic measurement. Our observation of topological links and Hopf fibration in a quantum simulator opens the door to probe rich topological properties of Hopf insulators in experiments. The quantum simulation and probing methods are also applicable to the study of other intricate three-dimensional topological model Hamiltonians.
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Received: 10 May 2017
Published: 23 May 2017
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| Fund: This work was supported by the grants from the Ministry of Science and Technology of China and the Ministry of Education. L.M.D. and S.T.W. acknowledge in addition support from the ARL and the AFOSR MURI programs. D.L.D. is supported by JQI-NSF-PFC and LPS-MPO-CMTC. |
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