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Interferometric braiding of anyons in Chern insulators

F. A. Palm1,2,3,5, N. Mostaan1,2,3, N. Goldman3,4,5, and F. Grusdt1,2

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Phys. Rev. B 113, 155419 – Published 13 April, 2026

DOI: https://doi.org/10.1103/mmhn-1c2c

Abstract

The coherent control and braiding of anyons remain central challenges in realizing topologically protected quantum operations. We propose a Ramsey interferometry protocol to directly access the geometric phases associated with anyons in fractional Chern insulators. Our approach employs impurities with individually addressable internal states that bind to the anyons, allowing their adiabatic motion and exchange under full spatial control. By combining Ramsey and spin-echo sequences using one and two impurities, the protocol gives independent access to the Aharonov-Bohm and exchange contributions to the total geometric phase, thereby providing an unambiguous probe of anyonic statistics. Our scheme can potentially be implemented in cold-atom quantum simulators as well as in van der Waals heterostructures. Complementary finite-size simulations in noninteracting Chern insulators quantify the system sizes required to faithfully extract geometric phases, highlighting the role of edge effects. Our results establish impurity-based interferometry as a feasible route toward direct anyon braiding experiments in quantum simulators and lay the groundwork for future explorations of non-Abelian braiding and topological quantum control.

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References (48)

  1. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).
  2. K. Kobayashi and M. Hashisaka, Shot noise in mesoscopic systems: From single particles to quantum liquids, J. Phys. Soc. Jpn. 90, 102001 (2021).
  3. T. Jonckheere, J. Rech, B. Grémaud, and T. Martin, Anyonic statistics revealed by the Hong-Ou-Mandel dip for fractional excitations, Phys. Rev. Lett. 130, 186203 (2023).
  4. Y. Ronen, T. Werkmeister, D. H. Najafabadi, A. T. Pierce, L. E. Anderson, Y. J. Shin, S. Y. Lee, Y. H. Lee, B. Johnson, K. Watanabe, T. Taniguchi, A. Yacoby, and P. Kim, Aharonov-Bohm effect in graphene-based Fabry-Pérot quantum Hall interferometers, Nat. Nanotechnol. 16, 563 (2021).
  5. M. Ruelle, E. Frigerio, J.-M. Berroir, B. Plaçais, J. Rech, A. Cavanna, U. Gennser, Y. Jin, and G. Fève, Comparing fractional quantum Hall Laughlin and Jain topological orders with the anyon collider, Phys. Rev. X 13, 011031 (2023).
  6. P. Glidic, O. Maillet, A. Aassime, C. Piquard, A. Cavanna, U. Gennser, Y. Jin, A. Anthore, and F. Pierre, Cross-correlation investigation of anyon statistics in the ν=1/3 and ν=2/5 fractional quantum Hall states, Phys. Rev. X 13, 011030 (2023).
  7. D. E. Feldman and B. I. Halperin, Fractional charge and fractional statistics in the quantum Hall effects, Rep. Prog. Phys. 84, 076501 (2021).
  8. C. Lin, M. Hashisaka, T. Akiho, K. Muraki, and T. Fujisawa, Quantized charge fractionalization at quantum Hall Y junctions in the disorder dominated regime, Nat. Commun. 12, 131 (2021).
  9. H. Bartolomei, M. Kumar, R. Bisognin, A. Marguerite, J.-M. Berroir, E. Bocquillon, B. Plaçais, A. Cavanna, Q. Dong, U. Gennser, Y. Jin, and G. Fève, Fractional statistics in anyon collisions, Science 368, 173 (2020).
  10. J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, Direct observation of anyonic braiding statistics, Nat. Phys. 16, 931 (2020).
  11. J.-Y. M. Lee, C. Hong, T. Alkalay, N. Schiller, V. Umansky, M. Heiblum, Y. Oreg, and H.-S. Sim, Partitioning of diluted anyons reveals their braiding statistics, Nature (London) 617, 277 (2023).
  12. K. J. Satzinger, Y.-J. Liu, A. Smith, C. Knapp, M. Newman, C. Jones, Z. Chen, C. Quintana, X. Mi, A. Dunsworth, et al., Realizing topologically ordered states on a quantum processor, Science 374, 1237 (2021).
  13. M. Iqbal, N. Tantivasadakarn, R. Verresen, S. L. Campbell, J. M. Dreiling, C. Figgatt, J. P. Gaebler, J. Johansen, M. Mills, S. A. Moses, J. M. Pino, A. Ransford, M. Rowe, P. Siegfried, R. P. Stutz, M. Foss-Feig, A. Vishwanath, and H. Dreyer, Non-Abelian topological order and anyons on a trapped-ion processor, Nature (London) 626, 505 (2024).
  14. T. I. Andersen, Y. D. Lensky, K. Kechedzhi, I. K. Drozdov, A. Bengtsson, S. Hong, A. Morvan, X. Mi, A. Opremcak, R. Acharya, et al., Non-Abelian braiding of graph vertices in a superconducting processor, Nature (London) 618, 264 (2023).
  15. N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands for ultracold atoms, Rev. Mod. Phys. 91, 015005 (2019).
  16. T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91, 015006 (2019).
  17. M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, T. Menke, D. Borgnia, P. M. Preiss, F. Grusdt, A. M. Kaufman, and M. Greiner, Microscopy of the interacting Harper-Hofstadter model in the two-body limit, Nature (London) 546, 519 (2017).
  18. J. Léonard, S. Kim, J. Kwan, P. Segura, F. Grusdt, C. Repellin, N. Goldman, and M. Greiner, Realization of a fractional quantum Hall state with ultracold atoms, Nature (London) 619, 495 (2023).
  19. L. W. Clark, N. Schine, C. Baum, N. Jia, and J. Simon, Observation of Laughlin states made of light, Nature (London) 582, 41 (2020).
  20. P. Lunt, P. Hill, J. Reiter, P. M. Preiss, M. Gałka, and S. Jochim, Realization of a laughlin state of two rapidly rotating fermions, Phys. Rev. Lett. 133, 253401 (2024).
  21. C. Wang, F.-M. Liu, M.-C. Chen, H. Chen, X.-H. Zhao, C. Ying, Z.-X. Shang, J.-W. Wang, Y.-H. Huo, C.-Z. Peng, X. Zhu, C.-Y. Lu, and J.-W. Pan, Realization of fractional quantum Hall state with interacting photons, Science 384, 579 (2024).
  22. B. Paredes, P. Fedichev, J. I. Cirac, and P. Zoller, 12-anyons in small atomic Bose-Einstein condensates, Phys. Rev. Lett. 87, 010402 (2001).
  23. M. Račiūnas, F. N. Ünal, E. Anisimovas, and A. Eckardt, Creating, probing, and manipulating fractionally charged excitations of fractional Chern insulators in optical lattices, Phys. Rev. A 98, 063621 (2018).
  24. E. Macaluso, T. Comparin, R. O. Umucalılar, M. Gerster, S. Montangero, M. Rizzi, and I. Carusotto, Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study, Phys. Rev. Res. 2, 013145 (2020).
  25. B. Wang, X. Dong, and A. Eckardt, Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope, SciPost Phys. 12, 095 (2022).
  26. F. A. Palm, J. Kwan, B. Bakkali-Hassani, M. Greiner, U. Schollwöck, N. Goldman, and F. Grusdt, Growing extended Laughlin states in a quantum gas microscope: A patchwork construction, Phys. Rev. Res. 6, 013198 (2024).
  27. N. Mostaan, N. Goldman, A. İmamoğlu, and F. Grusdt, Anyon-trions in atomically thin semiconductor heterostructures, PRX Quantum 7, 010325 (2026).
  28. G. Wagner and T. Neupert, Sensing the binding and unbinding of anyons at impurities, Phys. Rev. Res. 8, 013263 (2026).
  29. F. Grusdt, N. Y. Yao, D. Abanin, M. Fleischhauer, and E. Demler, Interferometric measurements of many-body topological invariants using mobile impurities, Nat. Commun. 7, 11994 (2016).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/mmhn-1c2c for details on the impurity interferometry sequence and supporting data.
  31. G. Moore and N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. B 360, 362 (1991).
  32. V. Barbé, A. Ciamei, B. Pasquiou, L. Reichsöllner, F. Schreck, P. S. Żuchowski, and J. M. Hutson, Observation of Feshbach resonances between alkali and closed-shell atoms, Nat. Phys. 14, 881 (2018).
  33. A. Heinz, A. J. Park, N. Šantić, J. Trautmann, S. G. Porsev, M. S. Safronova, I. Bloch, and S. Blatt, State-dependent optical lattices for the strontium optical qubit, Phys. Rev. Lett. 124, 203201 (2020).
  34. A. Popert, Y. Shimazaki, M. Kroner, K. Watanabe, T. Taniguchi, A. Imamoglu, and T. Smolenski, Optical sensing of fractional quantum Hall effect in graphene, Nano Lett. 22, 7363 (2022).
  35. H. Cui, Q. Hu, X. Zhao, L. Ma, F. Jin, Q. Zhang, K. Watanabe, T. Taniguchi, J. Shan, K. F. Mak, et al., Interlayer Fermi polarons of excited exciton states in quantizing magnetic fields, Nano Lett. 24, 7077 (2024).
  36. B. Gao, M. Ghafariasl, M. J. Mehrabad, T.-S. Huang, L. Zhang, D. Session, P. Upadhyay, R. Ma, G. Alshalan, D. G. S. Forero, et al., Probing quantum anomalous Hall states in twisted bilayer WSe2 via attractive polaron spectroscopy, Phys. Rev. X (to be published).
  37. E. Kapit, P. Ginsparg, and E. Mueller, Non-Abelian braiding of lattice bosons, Phys. Rev. Lett. 108, 066802 (2012).
  38. R. Resta, Macroscopic polarization in crystalline dielectrics: The geometric phase approach, Rev. Mod. Phys. 66, 899 (1994).
  39. A. S. Sørensen, E. Demler, and M. D. Lukin, Fractional quantum Hall states of atoms in optical lattices, Phys. Rev. Lett. 94, 086803 (2005).
  40. M. Hafezi, A. S. Sørensen, E. Demler, and M. D. Lukin, Fractional quantum Hall effect in optical lattices, Phys. Rev. A 76, 023613 (2007).
  41. R. N. Palmer, A. Klein, and D. Jaksch, Optical lattice quantum Hall effect, Phys. Rev. A 78, 013609 (2008).
  42. G. Möller and N. R. Cooper, Composite fermion theory for bosonic quantum Hall states on lattices, Phys. Rev. Lett. 103, 105303 (2009).
  43. D. Hügel, Hugo U. R. Strand, P. Werner, and L. Pollet, Anisotropic Harper-Hofstadter-Mott model: Competition between condensation and magnetic fields, Phys. Rev. B 96, 054431 (2017).
  44. Y.-C. He, F. Grusdt, A. Kaufman, M. Greiner, and A. Vishwanath, Realizing and adiabatically preparing bosonic integer and fractional quantum Hall states in optical lattices, Phys. Rev. B 96, 201103(R) (2017).
  45. X.-Y. Dong, A. G. Grushin, J. Motruk, and F. Pollmann, Charge excitation dynamics in bosonic fractional Chern insulators, Phys. Rev. Lett. 121, 086401 (2018).
  46. C. Repellin, J. Léonard, and N. Goldman, Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles, Phys. Rev. A 102, 063316 (2020).
  47. F. A. Palm, S. Mardazad, A. Bohrdt, U. Schollwöck, and F. Grusdt, Snapshot-based detection of ν=12 Laughlin states: Coupled chains and central charge, Phys. Rev. B 106, L081108 (2022).
  48. A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303, 2 (2003).

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Phys. Rev. B 113, 155419– Published 13 April, 2026
  • Received 16 December 2025
  • Accepted 20 March 2026
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