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  • Letter
  • Open Access

Controllable operations of edge states in cross-one-dimensional topological chains

Xian-Liang Lu1,2 and Ze-Liang Xiang1,3,*

  • *Contact author: xiangzliang@mail.sysu.edu.cn
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Phys. Rev. Research 7, L042050 – Published 3 December, 2025

DOI: https://doi.org/10.1103/ylrq-98wl

Abstract

Topological edge states have recently attracted intense interest due to their robustness in the presence of disorder and defects. However, most approaches for manipulating such states require global modulations of the system's Hamiltonian. In this work, we develop a method to control edge states using local interactions of a four-node junction between cross-one-dimensional topological atomic chains. These junction interactions can give rise to tunable couplings between the hybridized edge states within different geometric symmetries, allowing us to implement robust quantum state transfer and swap gate between the two topological chains via a double-quench protocol. Moreover, when the atoms in chains are precisely positioned and coupled to waveguides, the correlated decay caused by the environment enables the symmetric edge states to present subradiant dynamics and thus show extremely long coherence time. These findings open up possibilities for future quantum technologies with topological edge states.

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References (70)

  1. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  2. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  3. B. I. Halperin, Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential, Phys. Rev. B 25, 2185 (1982).
  4. Q. Niu and D. J. Thouless, Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction, J. Phys. A: Math. Gen. 17, 2453 (1984).
  5. M. Büttiker, Absence of backscattering in the quantum Hall effect in multiprobe conductors, Phys. Rev. B 38, 9375 (1988).
  6. M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, Robust optical delay lines with topological protection, Nat. Phys. 7, 907 (2011).
  7. J. Perczel, J. Borregaard, D. E. Chang, H. Pichler, S. F. Yelin, P. Zoller, and M. D. Lukin, Topological quantum optics in two-dimensional atomic arrays, Phys. Rev. Lett. 119, 023603 (2017).
  8. M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science 359, eaar4005 (2018).
  9. S. Ryu and Y. Hatsugai, Topological origin of zero-energy edge states in particle-hole symmetric systems, Phys. Rev. Lett. 89, 077002 (2002).
  10. J. K. Asbóth, L. Oroszlány, and A. Pályi, A Short Course on Topological Insulators (Springer International Publishing, Cham, 2016).
  11. W. Nie and Y.-X. Liu, Bandgap-assisted quantum control of topological edge states in a cavity, Phys. Rev. Res. 2, 012076(R) (2020).
  12. N. Y. Yao, C. R. Laumann, A. V. Gorshkov, H. Weimer, L. Jiang, J. I. Cirac, P. Zoller, and M. D. Lukin, Topologically protected quantum state transfer in a chiral spin liquid, Nat. Commun. 4, 1585 (2013).
  13. C. Dlaska, B. Vermersch, and P. Zoller, Robust quantum state transfer via topologically protected edge channels in dipolar arrays, Quantum Sci. Technol. 2, 015001 (2017).
  14. N. Lang and H. P. Büchler, Topological networks for quantum communication between distant qubits, npj Quantum Inf. 3, 47 (2017).
  15. F. Mei, G. Chen, L. Tian, S.-L. Zhu, and S. Jia, Robust quantum state transfer via topological edge states in superconducting qubit chains, Phys. Rev. A 98, 012331 (2018).
  16. S. Longhi, G. L. Giorgi, and R. Zambrini, Landau–Zener topological quantum state transfer, Adv. Quantum Technol. 2, 1800090 (2019).
  17. F. M. D’Angelis, F. A. Pinheiro, D. Guéry-Odelin, S. Longhi, and F. Impens, Fast and robust quantum state transfer in a topological Su-Schrieffer-Heeger chain with next-to-nearest-neighbor interactions, Phys. Rev. Res. 2, 033475 (2020).
  18. L. Qi, Y. Yan, Y. Xing, X.-D. Zhao, S. Liu, W.-X. Cui, X. Han, S. Zhang, and H.-F. Wang, Topological router induced via long-range hopping in a Su-Schrieffer-Heeger chain, Phys. Rev. Res. 3, 023037 (2021).
  19. J. Alicea, Y. Oreg, G. Refael, F. von Oppen, and M. P. A. Fisher, Non-Abelian statistics and topological quantum information processing in 1D wire networks, Nat. Phys. 7, 412 (2011).
  20. S. D. Sarma, M. Freedman, and C. Nayak, Majorana zero modes and topological quantum computation, npj Quantum Inf. 1, 15001 (2015).
  21. T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonderson, M. B. Hastings, C. Nayak, J. Alicea, K. Flensberg, S. Plugge, Y. Oreg, C. M. Marcus, and M. H. Freedman, Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes, Phys. Rev. B 95, 235305 (2017).
  22. I. Brouzos, I. Kiorpelidis, F. K. Diakonos, and G. Theocharis, Fast, robust, and amplified transfer of topological edge modes on a time-varying mechanical chain, Phys. Rev. B 102, 174312 (2020).
  23. T. Tian, Y. Zhang, L. Zhang, L. Wu, S. Lin, J. Zhou, C.-K. Duan, J.-H. Jiang, and J. Du, Experimental realization of nonreciprocal adiabatic transfer of phonons in a dynamically modulated nanomechanical topological insulator, Phys. Rev. Lett. 129, 215901 (2022).
  24. P. Pakkiam, N. P. Kumar, M. Pletyukhov, and A. Fedorov, Qubit-controlled directional edge states in waveguide QED, npj Quantum Inf. 9, 53 (2023).
  25. D. J. Thouless, Quantization of particle transport, Phys. Rev. B 27, 6083 (1983).
  26. M. Lohse, C. Schweizer, O. Zilberberg, M. Aidelsburger, and I. Bloch, A Thouless quantum pump with ultracold bosonic atoms in an optical superlattice, Nat. Phys. 12, 350 (2016).
  27. S. Nakajima, T. Tomita, S. Taie, T. Ichinose, H. Ozawa, L. Wang, M. Troyer, and Y. Takahashi, Topological Thouless pumping of ultracold fermions, Nat. Phys. 12, 296 (2016).
  28. X. Gu, S. Chen, and Y.-X. Liu, Topological edge states and pumping in a chain of coupled superconducting qubits, arXiv:1711.06829.
  29. S. Longhi, Topological pumping of edge states via adiabatic passage, Phys. Rev. B 99, 155150 (2019).
  30. Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, Topological states and adiabatic pumping in quasicrystals, Phys. Rev. Lett. 109, 106402 (2012).
  31. M. Verbin, O. Zilberberg, Y. Lahini, Y. E. Kraus, and Y. Silberberg, Topological pumping over a photonic Fibonacci quasicrystal, Phys. Rev. B 91, 064201 (2015).
  32. O. Zilberberg, S. Huang, J. Guglielmon, M. Wang, K. P. Chen, Y. E. Kraus, and M. C. Rechtsman, Photonic topological boundary pumping as a probe of 4D quantum Hall physics, Nature (London) 553, 59 (2018).
  33. Q. Cheng, H. Wang, Y. Ke, T. Chen, Y. Yu, Y. S. Kivshar, C. Lee, and Y. Pan, Asymmetric topological pumping in nonparaxial photonics, Nat. Commun. 13, 249 (2022).
  34. M. I. N. Rosa, R. K. Pal, J. R. F. Arruda, and M. Ruzzene, Edge states and topological pumping in spatially modulated elastic lattices, Phys. Rev. Lett. 123, 034301 (2019).
  35. I. H. Grinberg, M. Lin, C. Harris, W. A. Benalcazar, C. W. Peterson, T. L. Hughes, and G. Bahl, Robust temporal pumping in a magneto-mechanical topological insulator, Nat. Commun. 11, 974 (2020).
  36. Y. Xia, E. Riva, M. I. N. Rosa, G. Cazzulani, A. Erturk, F. Braghin, and M. Ruzzene, Experimental observation of temporal pumping in electromechanical waveguides, Phys. Rev. Lett. 126, 095501 (2021).
  37. W. Cheng, E. Prodan, and C. Prodan, Experimental demonstration of dynamic topological pumping across incommensurate bilayered acoustic metamaterials, Phys. Rev. Lett. 125, 224301 (2020).
  38. Z.-G. Chen, W. Tang, R.-Y. Zhang, Z. Chen, and G. Ma, Landau-Zener transition in the dynamic transfer of acoustic topological states, Phys. Rev. Lett. 126, 054301 (2021).
  39. H. Chen, H. Zhang, Q. Wu, Y. Huang, H. Nguyen, E. Prodan, X. Zhou, and G. Huang, Creating synthetic spaces for higher-order topological sound transport, Nat. Commun. 12, 5028 (2021).
  40. V. Lahtinen and J. K. Pachos, A short introduction to topological quantum computation, SciPost Phys. 3, 021 (2017).
  41. P. Boross, J. K. Asbóth, G. Széchenyi, L. Oroszlány, and A. Pályi, Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model, Phys. Rev. B 100, 045414 (2019).
  42. M. S. Scheurer and A. Shnirman, Nonadiabatic processes in Majorana qubit systems, Phys. Rev. B 88, 064515 (2013).
  43. L. Privitera, A. Russomanno, R. Citro, and G. E. Santoro, Nonadiabatic breaking of topological pumping, Phys. Rev. Lett. 120, 106601 (2018).
  44. P. Delplace, D. Ullmo, and G. Montambaux, Zak phase and the existence of edge states in graphene, Phys. Rev. B 84, 195452 (2011).
  45. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
  46. Z.-L. Xiang, S. Ashhab, J. Q. You, and F. Nori, Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems, Rev. Mod. Phys. 85, 623 (2013).
  47. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ylrq-98wl for details, including the derivation of the effective Hamiltonian based on symmetry analysis and photon-mediated super/subradiance of edge states, the evaluation of the swap gate, the remote entanglement generation protocol, and a brief discussion about the experimental implementation in superconducting circuits.
  48. J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88, 035005 (2016).
  49. O. Viyuela, A. Rivas, and M. A. Martin-Delgado, Uhlmann phase as a topological measure for one-dimensional fermion systems, Phys. Rev. Lett. 112, 130401 (2014).
  50. J. C. Budich and S. Diehl, Topology of density matrices, Phys. Rev. B 91, 165140 (2015).
  51. B. Monserrat and D. Vanderbilt, Temperature effects in the band structure of topological insulators, Phys. Rev. Lett. 117, 226801 (2016).
  52. Y. P. Kandel, H. Qiao, S. Fallahi, G. C. Gardner, M. J. Manfra, and J. M. Nichol, Coherent spin-state transfer via Heisenberg exchange, Nature (London) 573, 553 (2019).
  53. M. Bello, G. Platero, J. I. Cirac, and A. González-Tudela, Unconventional quantum optics in topological waveguide QED, Sci. Adv. 5, eaaw0297 (2019).
  54. W. Nie, Z. H. Peng, F. Nori, and Y.-x. Liu, Topologically protected quantum coherence in a superatom, Phys. Rev. Lett. 124, 023603 (2020).
  55. C. McDonnell and B. Olmos, Subradiant edge states in an atom chain with waveguide-mediated hopping, Quantum 6, 805 (2022).
  56. W. Nie, M. Antezza, Y.-x. Liu, and F. Nori, Dissipative topological phase transition with strong system-environment coupling, Phys. Rev. Lett. 127, 250402 (2021).
  57. R. H. Lehmberg, Radiation from an N-atom system. I. General formalism, Phys. Rev. A 2, 883 (1970).
  58. H. T. Dung, L. Knöll, and D.-G. Welsch, Resonant dipole-dipole interaction in the presence of dispersing and absorbing surroundings, Phys. Rev. A 66, 063810 (2002).
  59. Z. Ficek and R. Tanaś, Entangled states and collective nonclassical effects in two-atom systems, Phys. Rep. 372, 369 (2002).
  60. F. Le Kien, S. D. Gupta, K. P. Nayak, and K. Hakuta, Nanofiber-mediated radiative transfer between two distant atoms, Phys. Rev. A 72, 063815 (2005).
  61. A. Gonzalez-Tudela, D. Martin-Cano, E. Moreno, L. Martin-Moreno, C. Tejedor, and F. J. Garcia-Vidal, Entanglement of two qubits mediated by one-dimensional plasmonic waveguides, Phys. Rev. Lett. 106, 020501 (2011).
  62. D. E. Chang, L. Jiang, A. V. Gorshkov, and H. J. Kimble, Cavity QED with atomic mirrors, New J. Phys. 14, 063003 (2012).
  63. K. Lalumière, B. C. Sanders, A. F. van Loo, A. Fedorov, A. Wallraff, and A. Blais, Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms, Phys. Rev. A 88, 043806 (2013).
  64. P. Doyeux, S. A. H. Gangaraj, G. W. Hanson, and M. Antezza, Giant interatomic energy-transport amplification with nonreciprocal photonic topological insulators, Phys. Rev. Lett. 119, 173901 (2017).
  65. M. Mirhosseini, E. Kim, X. Zhang, A. Sipahigil, P. B. Dieterle, A. J. Keller, A. Asenjo-Garcia, D. E. Chang, and O. Painter, Cavity quantum electrodynamics with atom-like mirrors, Nature (London) 569, 692 (2019).
  66. P. Y. Wen, K.-T. Lin, A. F. Kockum, B. Suri, H. Ian, J. C. Chen, S. Y. Mao, C. C. Chiu, P. Delsing, F. Nori, G.-D. Lin, and I.-C. Hoi, Large collective Lamb shift of two distant superconducting artificial atoms, Phys. Rev. Lett. 123, 233602 (2019).
  67. A. F. van Loo, A. Fedorov, K. Lalumière, B. C. Sanders, A. Blais, and A. Wallraff, Photon-mediated interactions between distant artificial atoms, Science 342, 1494 (2013).
  68. A. Asenjo-Garcia, J. D. Hood, D. E. Chang, and H. J. Kimble, Atom-light interactions in quasi-one-dimensional nanostructures: A Green's-function perspective, Phys. Rev. A 95, 033818 (2017).
  69. Y.-X. Zhang and K. Mølmer, Theory of subradiant states of a one-dimensional two-level atom chain, Phys. Rev. Lett. 122, 203605 (2019).
  70. M. Zanner, T. Orell, C. M. F. Schneider, R. Albert, S. Oleschko, M. L. Juan, M. Silveri, and G. Kirchmair, Coherent control of a multi-qubit dark state in waveguide quantum electrodynamics, Nat. Phys. 18, 538 (2022).

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Phys. Rev. Research 7, L042050– Published 3 December, 2025
  • Received 14 August 2023
  • Accepted 1 November 2025
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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.

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