- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Proposal for realization and detection of Kitaev quantum spin liquid with Rydberg atoms

Yi-Hong Chen1,2,*, Bao-Zong Wang1,2,*, Ting-Fung Jeffrey Poon1,2, Xin-Chi Zhou1,2, Zheng-Xin Liu3, and Xiong-Jun Liu1,2,4,5,†

  • 1International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
  • 2Hefei National Laboratory, Hefei 230088, China
  • 3Department of Physics, Renmin University of China, Beijing 100872, China
  • 4International Quantum Academy, Shenzhen 518048, China
  • 5CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China

  • *These authors contributed equally to this work.
  • †Contact author: xiongjunliu@pku.edu.cn
PDF

Phys. Rev. Research 6, L042054 – Published 2 December, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042054

Abstract

The Kitaev chiral spin liquid has captured widespread interest in recent decades because of its intrinsic non-Abelian excitations, yet the experimental realization is challenging. Here we propose to realize and detect Kitaev chiral spin liquid in a deformed honeycomb array of Rydberg atoms. With a laser-assisted dipole-dipole interaction mechanism which realizes both effective hopping and pairing terms for hard-core bosons, together with van der Waals interactions, we achieve the pure Kitaev model with high precision. The gapped non-Abelian spin liquid phase is then obtained under experimental conditions. Moreover, we propose innovative strategies to probe the chiral Majorana edge modes by light Bragg scattering and by imagining their chiral motion. Our proposed scheme broadens the range of quantum spin models with exotic topological phases that can be realized and detected in atomic systems, and makes an important step toward manipulating non-Abelian anyons.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (83)

  1. X.-G. Wen, Colloquium: Zoo of quantum-topological phases of matter, Rev. Mod. Phys. 89, 041004 (2017).
  2. A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. (NY) 321, 2 (2006).
  3. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. D. Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).
  4. F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific, Singapore, 1990), Vol. 5.
  5. A. Stern, Non-Abelian states of matter, Nature (London) 464, 187 (2010).
  6. G. Moore and N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. B 360, 362 (1991).
  7. X.-G. Wen, Non-Abelian statistics in the fractional quantum Hall states, Phys. Rev. Lett. 66, 802 (1991).
  8. A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. (NY) 303, 2 (2003).
  9. J. K. Pachos, Introduction to Topological Quantum Computation (Cambridge University Press, Cambridge, England, 2012).
  10. A. Stern and N. H. Lindner, Topological quantum computation–from basic concepts to first experiments, Science 339, 1179 (2013).
  11. M. Hermanns, I. Kimchi, and J. Knolle, Physics of the Kitaev model: Fractionalization, dynamic correlations, and material connections, Annu. Rev. Condens. Matter Phys. 9, 17 (2018).
  12. J. Knolle and R. Moessner, A field guide to spin liquids, Annu. Rev. Condens. Matter Phys. 10, 451 (2019).
  13. H. Takagi, T. Takayama, G. Jackeli, G. Khaliullin, and S. E. Nagler, Concept and realization of Kitaev quantum spin liquids, Nat. Rev. Phys. 1, 264 (2019).
  14. S. Trebst and C. Hickey, Kitaev materials, Phys. Rep. 950, 1 (2022).
  15. A. Banerjee, J. Yan, J. Knolle, C. A. Bridges, M. B. Stone, M. D. Lumsden, D. G. Mandrus, D. A. Tennant, R. Moessner, and S. E. Nagler, Neutron scattering in the proximate quantum spin liquid α-RuCl3, Science 356, 1055 (2017).
  16. S.-H. Do, S.-Y. Park, J. Yoshitake, J. Nasu, Y. Motome, Y. S. Kwon, D. Adroja, D. Voneshen, K. Kim, T.-H. Jang et al., Majorana fermions in the Kitaev quantum spin system α-RuCl3, Nat. Phys. 13, 1079 (2017).
  17. Y. Kasahara, T. Ohnishi, Y. Mizukami, O. Tanaka, S. Ma, K. Sugii, N. Kurita, H. Tanaka, J. Nasu, Y. Motome et al., Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid, Nature (London) 559, 227 (2018).
  18. T. Yokoi, S. Ma, Y. Kasahara, S. Kasahara, T. Shibauchi, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, C. Hickey et al., Half-integer quantized anomalous thermal Hall effect in the Kitaev material candidate α-RuCl3, Science 373, 568 (2021).
  19. J. Bruin, R. Claus, Y. Matsumoto, N. Kurita, H. Tanaka, and H. Takagi, Robustness of the thermal Hall effect close to half-quantization in α-RuCl3, Nat. Phys. 18, 401 (2022).
  20. S.-H. Baek, S.-H. Do, K.-Y. Choi, Y. S. Kwon, A. U. B. Wolter, S. Nishimoto, J. van Den Brink, and B. Büchner, Evidence for a field-induced quantum spin liquid in α-RuCl3, Phys. Rev. Lett. 119, 037201 (2017).
  21. R. Hentrich, A. U. Wolter, X. Zotos, W. Brenig, D. Nowak, A. Isaeva, T. Doert, A. Banerjee, P. Lampen-Kelley, D. G. Mandrus et al., Unusual phonon heat transport in α-RuCl3: strong spin-phonon scattering and field-induced spin gap, Phys. Rev. Lett. 120, 117204 (2018).
  22. S. Bachus, D. A. S. Kaib, Y. Tokiwa, A. Jesche, V. Tsurkan, A. Loidl, S. M. Winter, A. A. Tsirlin, R. Valenti, and P. Gegenwart, Thermodynamic perspective on field-induced behavior of α-RuCl3, Phys. Rev. Lett. 125, 097203 (2020).
  23. I. A. Leahy, C. A. Pocs, P. E. Siegfried, D. Graf, S.-H. Do, K.-Y. Choi, B. Normand, and M. Lee, Anomalous thermal conductivity and magnetic torque response in the honeycomb magnet α-RuCl3, Phys. Rev. Lett. 118, 187203 (2017).
  24. N. Janša, A. Zorko, M. Gomilšek, M. Pregelj, K. W. Krämer, D. Biner, A. Biffin, C. Rüegg, and M. Klanjšek, Observation of two types of fractional excitation in the Kitaev honeycomb magnet, Nat. Phys. 14, 786 (2018).
  25. S. M. Winter, K. Riedl, D. Kaib, R. Coldea, and R. Valentí, Probing α-RuCl3 beyond magnetic order: Effects of temperature and magnetic field, Phys. Rev. Lett. 120, 077203 (2018).
  26. L. E. Chern, E. Z. Zhang, and Y. B. Kim, Sign structure of thermal Hall conductivity and topological magnons for in-plane field polarized Kitaev magnets, Phys. Rev. Lett. 126, 147201 (2021).
  27. I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
  28. A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pearson, M. Troyer, and P. Zoller, Practical quantum advantage in quantum simulation, Nature (London) 607, 667 (2022).
  29. L.-M. Duan, E. Demler, and M. D. Lukin, Controlling spin exchange interactions of ultracold atoms in optical lattices, Phys. Rev. Lett. 91, 090402 (2003).
  30. A. D. Bookatz, P. Wocjan, and L. Viola, Hamiltonian quantum simulation with bounded-strength controls, New J. Phys. 16, 045021 (2014).
  31. H. C. Po, L. Fidkowski, A. Vishwanath, and A. C. Potter, Radical chiral floquet phases in a periodically driven Kitaev model and beyond, Phys. Rev. B 96, 245116 (2017).
  32. M. Kalinowski, N. Maskara, and M. D. Lukin, Non-Abelian floquet spin liquids in a digital Rydberg simulator, Phys. Rev. X 13, 031008 (2023).
  33. B.-Y. Sun, N. Goldman, M. Aidelsburger, and M. Bukov, Engineering and probing non-Abelian chiral spin liquids using periodically driven ultracold atoms, PRX Quantum 4, 020329 (2023).
  34. A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020).
  35. A. W. Glaetzle, M. Dalmonte, R. Nath, I. Rousochatzakis, R. Moessner, and P. Zoller, Quantum spin-ice and Dimer models with Rydberg atoms, Phys. Rev. X 4, 041037 (2014).
  36. T. L. Nguyen, J.-M. Raimond, C. Sayrin, R. Cortinas, T. Cantat-Moltrecht, F. Assemat, I. Dotsenko, S. Gleyzes, S. Haroche, G. Roux et al., Towards quantum simulation with circular Rydberg atoms, Phys. Rev. X 8, 011032 (2018).
  37. A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. D. Lukin, and P. Zoller, Emerging two-dimensional gauge theories in Rydberg configurable arrays, Phys. Rev. X 10, 021057 (2020).
  38. P. P. Mazza, R. Schmidt, and I. Lesanovsky, Vibrational dressing in kinetically constrained Rydberg spin systems, Phys. Rev. Lett. 125, 033602 (2020).
  39. J. Y. Lee, J. Ramette, M. A. Metlitski, V. Vuletić, W. W. Ho, and S. Choi, Landau-forbidden quantum criticality in Rydberg quantum simulators, Phys. Rev. Lett. 131, 083601 (2023).
  40. N. Nishad, A. Keselman, T. Lahaye, A. Browaeys, and S. Tsesses, Quantum simulation of generic spin-exchange models in Floquet-engineered Rydberg-atom arrays, Phys. Rev. A 108, 053318 (2023).
  41. M. Kunimi, T. Tomita, H. Katsura, and Y. Kato, Proposal for simulating quantum spin models with the Dzyaloshinskii-Moriya interaction using Rydberg atoms and the construction of asymptotic quantum many-body scar states, Phys. Rev. A 110, 043312 (2024).
  42. D. Barredo, S. De Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays, Science 354, 1021 (2016).
  43. M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, Atom-by-atom assembly of defect-free one-dimensional cold atom arrays, Science 354, 1024 (2016).
  44. H. Kim, W. Lee, H.-g. Lee, H. Jo, Y. Song, and J. Ahn, In situ single-atom array synthesis using dynamic holographic optical tweezers, Nat. Commun. 7, 13317 (2016).
  45. D. Barredo, V. Lienhard, S. De Leseleuc, T. Lahaye, and A. Browaeys, Synthetic three-dimensional atomic structures assembled atom by atom, Nature (London) 561, 79 (2018).
  46. D. O. De Mello, D. Schäffner, J. Werkmann, T. Preuschoff, L. Kohfahl, M. Schlosser, and G. Birkl, Defect-free assembly of 2D clusters of more than 100 single-atom quantum systems, Phys. Rev. Lett. 122, 203601 (2019).
  47. M. Saffman, T. G. Walker, and K. Mølmer, Quantum information with Rydberg atoms, Rev. Mod. Phys. 82, 2313 (2010).
  48. H. Labuhn, D. Barredo, S. Ravets, S. De Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models, Nature (London) 534, 667 (2016).
  49. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner et al., Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
  50. A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pichler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev et al., Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator, Nature (London) 568, 207 (2019).
  51. P. Scholl, M. Schuler, H. J. Williams, A. A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T. C. Lang, T. Lahaye et al., Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms, Nature (London) 595, 233 (2021).
  52. S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Semeghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pichler, W. W. Ho et al., Quantum phases of matter on a 256-atom programmable quantum simulator, Nature (London) 595, 227 (2021).
  53. D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Semeghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho et al., Controlling quantum many-body dynamics in driven Rydberg atom arrays, Science 371, 1355 (2021).
  54. D. Barredo, H. Labuhn, S. Ravets, T. Lahaye, A. Browaeys, and C. S. Adams, Coherent excitation transfer in a spin chain of three Rydberg atoms, Phys. Rev. Lett. 114, 113002 (2015).
  55. C. Chen, G. Bornet, M. Bintz, G. Emperauger, L. Leclerc, V. S. Liu, P. Scholl, D. Barredo, J. Hauschild, S. Chatterjee et al., Continuous symmetry breaking in a two-dimensional Rydberg array, Nature (London) 616, 691 (2023).
  56. S. de Léséleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. Büchler, T. Lahaye, and A. Browaeys, Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms, Science 365, 775 (2019).
  57. G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar et al., Probing topological spin liquids on a programmable quantum simulator, Science 374, 1242 (2021).
  58. T.-H. Yang, B.-Z. Wang, X.-C. Zhou, and X.-J. Liu, Quantum Hall states for Rydberg arrays with laser-assisted dipole-dipole interactions, Phys. Rev. A 106, L021101 (2022).
  59. T. F. J. Poon, X.-C. Zhou, B.-Z. Wang, T.-H. Yang, and X.-J. Liu, Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms, Adv. Quantum Technol. 7, 2300356 (2024).
  60. X.-C. Zhou, Y. Wang, T.-F. J. Poon, Q. Zhou, and X.-J. Liu, Exact new mobility edges between critical and localized states, Phys. Rev. Lett. 131, 176401 (2023).
  61. M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Realization of the Hofstadter hamiltonian with ultracold atoms in optical lattices, Phys. Rev. Lett. 111, 185301 (2013).
  62. H. Miyake, G. A. Siviloglou, C. J. Kennedy, W. C. Burton, and W. Ketterle, Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices, Phys. Rev. Lett. 111, 185302 (2013).
  63. X.-J. Liu, K. T. Law, and T. K. Ng, Realization of 2D spin-orbit interaction and exotic topological orders in cold atoms, Phys. Rev. Lett. 112, 086401 (2014).
  64. M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. Cooper, I. Bloch, and N. Goldman, Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms, Nat. Phys. 11, 162 (2015).
  65. Z. Wu, L. Zhang, W. Sun, X.-T. Xu, B.-Z. Wang, S.-C. Ji, Y. Deng, S. Chen, X.-J. Liu, and J.-W. Pan, Realization of two-dimensional spin-orbit coupling for Bose-Einstein condensates, Science 354, 83 (2016).
  66. X.-J. Liu, Z.-X. Liu, K. T. Law, W. V. Liu, and T. K. Ng, Chiral topological orders in an optical Raman lattice, New J. Phys. 18, 035004 (2016).
  67. B. Song, L. Zhang, C. He, T. F. J. Poon, E. Hajiyev, S. Zhang, X.-J. Liu, and G.-B. Jo, Observation of symmetry-protected topological band with ultracold fermions, Sci. Adv. 4, eaao4748 (2018).
  68. Y.-H. Lu, B.-Z. Wang, and X.-J. Liu, Ideal Weyl semimetal with 3D spin-orbit coupled ultracold quantum gas, Sci. Bull. 65, 2080 (2020).
  69. Z.-Y. Wang, X.-C. Cheng, B.-Z. Wang, J.-Y. Zhang, Y.-H. Lu, C.-R. Yi, S. Niu, Y. Deng, X.-J. Liu, S. Chen et al., Realization of an ideal Weyl semimetal band in a quantum gas with 3D spin-orbit coupling, Science 372, 271 (2021).
  70. J+−γ (J−−γ) denote the hopping (pairing) term across the γ bond.
  71. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L042054 for about the laser assisted dipole-dipole interaction, numerical estimate of parameters, and the detection schemes, which includes Refs. [79, 80, 81, 82, 83].
  72. Z. Zhu, I. Kimchi, D. Sheng, and L. Fu, Robust non-Abelian spin liquid and a possible intermediate phase in the antiferromagnetic Kitaev model with magnetic field, Phys. Rev. B 97, 241110 (2018).
  73. S. R. Cohen and J. D. Thompson, Quantum computing with circular Rydberg atoms, PRX Quantum 2, 030322 (2021).
  74. J. Knolle, G.-W. Chern, D. Kovrizhin, R. Moessner, and N. Perkins, Raman scattering signatures of Kitaev spin liquids in A2IrO3 iridates with A =Na or Li, Phys. Rev. Lett. 113, 187201 (2014).
  75. X.-J. Liu, X. Liu, C. Wu, and J. Sinova, Quantum anomalous Hall effect with cold atoms trapped in a square lattice, Phys. Rev. A 81, 033622 (2010).
  76. T. D. Stanescu, V. Galitski, and S. D. Sarma, Topological states in two-dimensional optical lattices, Phys. Rev. A 82, 013608 (2010).
  77. N. Goldman, J. Beugnon, and F. Gerbier, Detecting chiral edge states in the Hofstadter optical lattice, Phys. Rev. Lett. 108, 255303 (2012).
  78. M. Buchhold, D. Cocks, and W. Hofstetter, Effects of smooth boundaries on topological edge modes in optical lattices, Phys. Rev. A 85, 063614 (2012).
  79. T. G. Walker and M. Saffman, Consequences of Zeeman degeneracy for the van der Waals blockade between Rydberg atoms, Phys. Rev. A 77, 032723 (2008).
  80. D. Barredo, V. Lienhard, P. Scholl, S. de Léséleuc, T. Boulier, A. Browaeys, and T. Lahaye, Three-dimensional trapping of individual Rydberg atoms in ponderomotive bottle beam traps, Phys. Rev. Lett. 124, 023201 (2020).
  81. Y. Mei, Y. Li, H. Nguyen, P. Berman, and A. Kuzmich, Trapped alkali-metal Rydberg qubit, Phys. Rev. Lett. 128, 123601 (2022).
  82. E. H. Lieb, Flux phase of the half-filled band, Phys. Rev. Lett. 73, 2158 (1994).
  83. F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett. 61, 2015 (1988).

Outline

Information

Phys. Rev. Research 6, L042054– Published 2 December, 2024
  • Received 12 November 2023
  • Revised 29 July 2024
  • Accepted 3 October 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation