Abstract
The observation of topological phases beyond two dimensions, as widely reported in solid-state systems1,2, has been an open challenge for ultracold atoms. Although many theoretical schemes have been proposed, the experimental complexity in realizing and characterizing the three-dimensional (3D) band structure has acted as a barrier against experiments achieving this. Here, we realize a 3D spinâorbit coupled nodal-line semimetal in an optical Raman lattice filled with ultracold fermions, and observe the bulk line nodes in the band structure. The realized topological semimetal exhibits an emergent magnetic group symmetry. This allows detection of the nodal lines by effectively reconstructing the 3D topological band from a series of measurements of integrated spin textures, which precisely render spin textures on the parameter-tuned magnetic-group-symmetric planes. The detection technique can be applied generally to explore 3D topological states of similar symmetries. Furthermore, we observe the band inversion lines from topological quench dynamics, which are bulk counterparts of Fermi arc states and connect the Dirac points, reconfirming the realized topological band. Our results demonstrate an approach to effectively observe 3D band topology, and open the way to probe exotic topological physics for ultracold atoms in high dimensions.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 /Â 30Â days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
References
Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057â1110 (2011).
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045â3067 (2010).
Liu, Z. K. et al. A stable three-dimensional topological dirac semimetal Cd3As2. Nat. Mater. 13, 677â681 (2014).
Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613â617 (2015).
Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).
Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012).
Nielsen, H. B. & Ninomiya, M. Absence of neutrinos on a lattice: (I). Proof by homotopy theory. Nucl. Phys. B 185, 20â40 (1981).
Fang, C., Chen, Y., Kee, H. Y. & Fu, L. Topological nodal line semimetals with and without spinâorbital coupling. Phys. Rev. B 92, 081201 (2015).
BzduÅ¡ek, T., Wu, Q., Rüegg, A., Sigrist, M. & Soluyanov, A. A. Nodal-chain metals. Nature 538, 75â78 (2016).
Juan, F., Grushin, A. G., Morimoto, T. & Moore, J. E. Quantized circular photogalvanic effect in Weyl semimetals. Nat. Commun. 8, 15995 (2017).
Lou, R. et al. Experimental observation of bulk nodal lines and electronic surface states in ZrB2. npj Quantum Mater. 3, 43 (2018).
Dalibard, J., Gerbier, F., JuzeliÅ«nas, G. & Oehberg, P. Colloquium: Artificial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523â1543 (2011).
Goldman, N., Juzeliunas, G., Ãhberg, P. & Spielman, I. B. Light-induced gauge fields for ultracold atoms. Rep. Prog. Phys. 77, 126401 (2014).
Zhai, H. Degenerate quantum gases with spinâorbit coupling: a review. Rep. Prog. Phys. 78, 026001 (2015).
Zhang, L. & Liu, X. -J. in Synthetic SpinâOrbit Coupling in Cold Atoms (eds Zhang, W. & Sa Melo, C. A. R.) Ch. 1, 1â87 (World Scientific, 2018).
Jotzu, G. et al. Experimental realization of the topological haldane model with ultracold fermions. Nature 515, 237â240 (2014).
Wu, Z. et al. Realization of two-dimensional spinâorbit coupling for BoseâEinstein condensates. Science 354, 83â88 (2016).
Liu, X.-J., Law, K. T. & Ng, T. K. Realization of 2D spinâorbit interaction and exotic topological orders in cold atoms. Phys. Rev. Lett. 112, 086401 (2014).
Li, J.-R. et al. A stripe phase with supersolid properties in spinâorbit-coupled BoseâEinstein condensates. Nature 543, 91â94 (2017).
Song, B. et al. Observation of symmetry-protected topological band with ultracold fermions. Sci. Adv. 4, eaao4748 (2018).
Xu, Y. & Duan, L. M. Type-II Weyl points in three-dimensional cold-atom optical lattices. Phys. Rev. A 94, 053619 (2016).
Xu, Y. & Zhang, C. Out-of-equilibrium open quantum systems: a comparison of approximate quantum master equation approaches with exact results. Phys. Rev. A 93, 063606 (2016).
Wang, Y. & Liu, X.-J. Predicted scaling behavior of bloch oscillation in Weyl semimetals. Phys. Rev. A 94, 031603(R) (2016).
He, W.-Y., Xu, D.-H., Zhou, B. T., Zhou, Q. & Law, K. T. From nodal-ring topological superfluids to spiral Majorana modes in cold atomic systems. Phys. Rev. A 97, 043618 (2018).
Wang, B.-Z. et al. Dirac-, Rashba- and Weyl-type spinâorbit couplings: toward experimental realization in ultracold atoms. Phys. Rev. A 97, 011605(R) (2018).
DubÄek, T. et al. Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space. Phys. Rev. Lett. 114, 225301 (2015).
Tran, D. T., Dauphin, A., Grushin, A. G., Zoller, P. & Goldman, N. Probing topology by heating: quantized circular dichroism in ultracold atoms. Sci. Adv. 3, e1701207 (2017).
Poon, T. F. J. & Liu, X.-J. From a semimetal to a chiral FuldeâFerrell superfluid. Phys. Rev. B 97, 020501(R) (2018).
Lin, Y. J., Jiménez-Garca, K. & Spielman, I. B. Spinâorbit-coupled BoseâEinstein condensates. Nature 471, 83â86 (2011).
Wang, P. et al. Spinâorbit coupled degenerate Fermi gases. Phys. Rev. Lett. 109, 095301 (2012).
Cheuk, L. W. et al. Spin-injection spectroscopy of a spinâorbit coupled Fermi gas. Phys. Rev. Lett. 109, 095302 (2012).
Song, B. et al. Spinâorbit-coupled two-electron Fermi gases of ytterbium atoms. Phys. Rev. A 94, 061604 (2016).
Zhang, L., Zhang, L., Niu, S. & Liu, X.-J. Dynamical classification of topological quantum phases. Sci. Bull. 63, 1385â1391 (2018).
Acknowledgements
The authors acknowledge valuable discussions with L. Zhang. This work was supported by the Joint Research Scheme sponsored by the Research Grants Council (RGC) of the Hong Kong and National Natural Science Foundation of China (NSFC) (project nos. N-HKUST601/17 and 11761161003). G.-B.J. acknowledges support from the RGC, the Croucher Foundation (ECS26300014, GRF16300215, GRF16311516, GRF16305317 and C6005-17G-A) and Croucher Innovation grants. G.-B.J also acknowledges partial support (SSTSP grant) from HKUST. X.-J.L. acknowledges support from the National Key R&D Program of China (2016YFA0301604), NSFC (11574008 and 11825401) and the Strategic Priority Research Program of the Chinese Academy of Science (grant no. XDB28000000).
Author information
Authors and Affiliations
Contributions
B.S., C.H. and Z.R. carried out the experiment and data analysis and helped with numerical calculations. S.N. proved the results of reconstructing the 3D band topology by 2D spin-texture imaging. S.N. and L.Z. performed theoretical modelling and numerical calculations. G.-B.J. and X.-J.L. conceived the project and supervised the research.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisherâs note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
Supplementary text, Supplementary Figs. 1â8 and Supplementary references.
Rights and permissions
About this article
Cite this article
Song, B., He, C., Niu, S. et al. Observation of nodal-line semimetal with ultracold fermions in an optical lattice. Nat. Phys. 15, 911â916 (2019). https://doi.org/10.1038/s41567-019-0564-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41567-019-0564-y
This article is cited by
-
Realization of highly isolated stable few-spin systems based on alkaline-earth fermions
Frontiers of Physics (2023)
-
Chiral control of quantum states in non-Hermitian spinâorbit-coupled fermions
Nature Physics (2022)
-
Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
npj Quantum Materials (2022)
-
âDesigning synthetic topological matter with atoms and lightsâ
Light: Science & Applications (2022)
-
Quantum simulations with multiphoton Fock states
npj Quantum Information (2021)