- 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
  • Open Access

Distributing entanglement at the quantum speed limit in Rydberg chains

Kent Ueno and Alexandre Cooper*

  • *Contact author: alexandre.cooper@uwaterloo.ca
PDF

Phys. Rev. Research 8, 023260 – Published 8 June, 2026

DOI: https://doi.org/10.1103/bzd3-m6p9

Abstract

We numerically study the transport of Rydberg excitations in chains of neutral atoms. We realize an effective flip-flop interaction using off-resonant driving fields. By tuning the relative distances between atoms and applying atom-selective detuning fields, we fulfill the perfect transport condition. This condition enables the transfer of a single Rydberg excitation from one end of the chain to the other, allowing the distribution of entanglement across the chain at the quantum speed limit. Through numerical simulations, we identify the set of control parameters that maximizes the transport probability under experimentally relevant conditions. We study the various competing trade-offs involved in the hierarchy of approximations used to map the native Rydberg spin model onto the effective model driving spin transport. Our results suggest that entanglement can be distributed over chains of more than 50 atoms spanning hundreds of microns at room temperature. This study informs the selection of parameters for the experimental realization of perfect transport in Rydberg chains, providing an approach to distribute entanglement among distant atoms in quantum processors.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (69)

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
  2. B. Schumacher, Sending entanglement through noisy quantum channels, Phys. Rev. A 54, 2614 (1996).
  3. S. Bose, Quantum communication through an unmodulated spin chain, Phys. Rev. Lett. 91, 207901 (2003).
  4. N. Y. Yao, L. Jiang, A. V. Gorshkov, Z.-X. Gong, A. Zhai, L.-M. Duan, and M. D. Lukin, Robust quantum state transfer in random unpolarized spin chains, Phys. Rev. Lett. 106, 040505 (2011).
  5. M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Perfect state transfer in quantum spin networks, Phys. Rev. Lett. 92, 187902 (2004).
  6. M. Christandl, N. Datta, T. C. Dorlas, A. Ekert, A. Kay, and A. J. Landahl, Perfect transfer of arbitrary states in quantum spin networks, Phys. Rev. A 71, 032312 (2005).
  7. M.-H. Yung, Quantum speed limit for perfect state transfer in one dimension, Phys. Rev. A 74, 030303(R) (2006).
  8. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70, 1895 (1993).
  9. R. J. Chapman, M. Santandrea, Z. Huang, G. Corrielli, A. Crespi, M.-H. Yung, R. Osellame, and A. Peruzzo, Experimental perfect state transfer of an entangled photonic qubit, Nat. Commun. 7, 11339 (2016).
  10. X. Li, Y. Ma, J. Han, T. Chen, Y. Xu, W. Cai, H. Wang, Y. P. Song, Z.-Y. Xue, Z.-Q. Yin, and L. Sun, Perfect quantum state transfer in a superconducting qubit chain with parametrically tunable couplings, Phys. Rev. Appl. 10, 054009 (2018).
  11. G. Ciaramicoli, I. Marzoli, and P. Tombesi, Spin chains with electrons in Penning traps, Phys. Rev. A 75, 032348 (2007).
  12. P. Cappellaro, C. Ramanathan, and D. G. Cory, Simulations of information transport in spin chains, Phys. Rev. Lett. 99, 250506 (2007).
  13. R. Blatt and C. F. Roos, Quantum simulations with trapped ions, Nat. Phys. 8, 277 (2012).
  14. P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, Strongly correlated quantum walks in optical lattices, Science 347, 1229 (2015).
  15. A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020).
  16. A. H. Karamlou, J. Braumüller, Y. Yanay, A. Di Paolo, P. M. Harrington, B. Kannan, D. Kim, M. Kjaergaard, A. Melville, S. Muschinske, B. M. Niedzielski, A. Vepsäläinen, R. Winik, J. L. Yoder, M. Schwartz, C. Tahan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Quantum transport and localization in 1d and 2d tight-binding lattices, npj Quantum Inf. 8, 35 (2022).
  17. A. Ungar, P. Cappellaro, A. Cooper, and W. K. C. Sun, Control of an environmental spin defect beyond the coherence limit of a central spin, PRX Quantum 5, 010321 (2024).
  18. E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, Observation of Rydberg blockade between two atoms, Nat. Phys. 5, 110 (2009).
  19. H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
  20. D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, Synthetic three-dimensional atomic structures assembled atom by atom, Nature (London) 561, 79 (2018).
  21. S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Semeghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pichler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuletić, and M. D. Lukin, Quantum phases of matter on a 256-atom programmable quantum simulator, Nature (London) 595, 227 (2021).
  22. D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, et al., A quantum processor based on coherent transport of entangled atom arrays, Nature (London) 604, 451 (2022).
  23. J.-L. Wu, Y. Wang, J.-X. Han, Y.-K. Feng, S.-L. Su, Y. Xia, Y. Jiang, and J. Song, One-step implementation of Rydberg-antiblockade swap and controlled-swap gates with modified robustness, Photon. Res. 9, 814 (2021).
  24. Y. Xiao, Y.-H. Kang, R.-H. Zheng, J. Song, Y.-H. Chen, and Y. Xia, Effective nonadiabatic holonomic swap gate with Rydberg atoms using invariant-based reverse engineering, Phys. Rev. A 109, 062610 (2024).
  25. Y. Wang, J. Wang, A. Panja, X. Wang, and Q.-Y. Liang, Directional transport in Rydberg atom arrays via kinetic constraints and temporal modulation, Phys. Rev. Res. 7, L022035 (2025).
  26. D. Schäffner, T. Preuschoff, S. Ristok, L. Brozio, M. Schlosser, H. Giessen, and G. Birkl, Arrays of individually controllable optical tweezers based on 3D-printed microlens arrays, Opt. Express 28, 8640 (2020).
  27. A. Holman, Y. Xu, X. Sun, J. Wu, M. Wang, Z. Zhu, B. Seo, N. Yu, and S. Will, Trapping of single atoms in metasurface optical tweezer arrays, Nature (London) 649, 859 (2026).
  28. See Supplemental Material at http://link.aps.org/supplemental/10.1103/bzd3-m6p9 for details on the estimation of transport speeds and numerical methods for solving the inversion problem, which includes Refs. [22, 23, 24, 25, 45, 69].
  29. F. Yang, S. Yang, and L. You, Quantum transport of Rydberg excitons with synthetic spin-exchange interactions, Phys. Rev. Lett. 123, 063001 (2019).
  30. K. Kim, F. Yang, K. Mølmer, and J. Ahn, Realization of an extremely anisotropic Heisenberg magnet in Rydberg atom arrays, Phys. Rev. X 14, 011025 (2024).
  31. 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).
  32. A. Guttridge, D. K. Ruttley, A. C. Baldock, R. González-Férez, H. R. Sadeghpour, C. S. Adams, and S. L. Cornish, Observation of Rydberg blockade due to the charge-dipole interaction between an atom and a polar molecule, Phys. Rev. Lett. 131, 013401 (2023).
  33. I. I. Beterov, I. I. Ryabtsev, D. B. Tretyakov, and V. M. Entin, Quasiclassical calculations of blackbody-radiation-induced depopulation rates and effective lifetimes of Rydberg nS, nP, and nD alkali-metal atoms with n≤80, Phys. Rev. A 79, 052504 (2009).
  34. A. G. de Oliveira, E. Diamond-Hitchcock, D. M. Walker, M. T. Wells-Pestell, G. Pelegrí, C. J. Picken, G. P. A. Malcolm, A. J. Daley, J. Bass, and J. D. Pritchard, Demonstration of weighted-graph optimization on a Rydberg-atom array using local light shifts, PRX Quantum 6, 010301 (2025).
  35. C. Di Franco, M. Paternostro, D. I. Tsomokos, and S. F. Huelga, Control-limited perfect state transfer, quantum stochastic resonance, and many-body entangling gate in imperfect qubit registers, Phys. Rev. A 77, 062337 (2008).
  36. C. Di Franco, M. Paternostro, and M. S. Kim, Perfect state transfer on a spin chain without state initialization, Phys. Rev. Lett. 101, 230502 (2008).
  37. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940).
  38. M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Bloch oscillations of atoms in an optical potential, Phys. Rev. Lett. 76, 4508 (1996).
  39. P. Jordan and E. Wigner, Über das Paulische Äquivalenzverbot, Z. Phys. 47, 631 (1928).
  40. E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys. (NY) 16, 407 (1961).
  41. A. Kay, Perfect state transfer: Beyond nearest-neighbor couplings, Phys. Rev. A 73, 032306 (2006).
  42. R. J. Cook and B. W. Shore, Coherent dynamics of N-level atoms and molecules. III. An analytically soluble periodic case, Phys. Rev. A 20, 539 (1979).
  43. N. Šibalić, J. Pritchard, C. Adams, and K. Weatherill, ARC: An open-source library for calculating properties of alkali Rydberg atoms, Comput. Phys. Commun. 220, 319 (2017).
  44. T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, Evidence of antiblockade in an ultracold Rydberg gas, Phys. Rev. Lett. 104, 013001 (2010).
  45. J. R. Johansson, P. D. Nation, and F. Nori, QuTiP 2: A Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 184, 1234 (2013).
  46. A. Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77, 1413 (1996).
  47. M. Horodecki, P. Horodecki, and R. Horodecki, Separability of mixed states: Necessary and sufficient conditions, Phys. Lett. A 223, 1 (1996).
  48. W. K. C. Sun, A. Cooper, and P. Cappellaro, Improved entanglement detection with subspace witnesses, Phys. Rev. A 101, 012319 (2020).
  49. W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998).
  50. K.-N. Schymik, S. Pancaldi, F. Nogrette, D. Barredo, J. Paris, A. Browaeys, and T. Lahaye, Single atoms with 6000-second trapping lifetimes in optical-tweezer arrays at cryogenic temperatures, Phys. Rev. Appl. 16, 034013 (2021).
  51. M. Marcuzzi, J. Minář, D. Barredo, S. de Léséleuc, H. Labuhn, T. Lahaye, A. Browaeys, E. Levi, and I. Lesanovsky, Facilitation dynamics and localization phenomena in Rydberg lattice gases with position disorder, Phys. Rev. Lett. 118, 063606 (2017).
  52. H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, High-fidelity control and entanglement of Rydberg-atom qubits, Phys. Rev. Lett. 121, 123603 (2018).
  53. A. M. Kaufman, B. J. Lester, and C. A. Regal, Cooling a single atom in an optical tweezer to its quantum ground state, Phys. Rev. X 2, 041014 (2012).
  54. J. D. Thompson, T. G. Tiecke, A. S. Zibrov, V. Vuletić, and M. D. Lukin, Coherence and Raman sideband cooling of a single atom in an optical tweezer, Phys. Rev. Lett. 110, 133001 (2013).
  55. N.-C. Chiu, E. C. Trapp, J. Guo, M. H. Abobeih, L. M. Stewart, S. Hollerith, P. L. Stroganov, M. Kalinowski, A. A. Geim, S. J. Evered, S. H. Li, X. Lyu, L. M. Peters, D. Bluvstein, T. T. Wang, M. Greiner, V. Vuletić, and M. D. Lukin, Continuous operation of a coherent 3,000-qubit system, Nature (London) 646, 1075 (2025).
  56. C. Wyenberg, K. Ueno, and A. Cooper, Quantum channel for modeling spin-motion dephasing in Rydberg chains, arXiv:2506.24082.
  57. G. Günter, H. Schempp, M. R. de Saint-Vincent, V. Gavryusev, S. Helmrich, C. S. Hofmann, S. Whitlock, and M. Weidemüller, Observing the dynamics of dipole-mediated energy transport by interaction-enhanced imaging, Science 342, 954 (2013).
  58. D. W. Schönleber, A. Eisfeld, M. Genkin, S. Whitlock, and S. Wüster, Quantum simulation of energy transport with embedded Rydberg aggregates, Phys. Rev. Lett. 114, 123005 (2015).
  59. 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).
  60. A. P. Orioli, A. Signoles, H. Wildhagen, G. Günter, J. Berges, S. Whitlock, and M. Weidemüller, Relaxation of an isolated dipolar-interacting Rydberg quantum spin system, Phys. Rev. Lett. 120, 063601 (2018).
  61. H. Schempp, G. Günter, S. Wüster, M. Weidemüller, and S. Whitlock, Correlated exciton transport in Rydberg-dressed-atom spin chains, Phys. Rev. Lett. 115, 093002 (2015).
  62. F. Letscher and D. Petrosyan, Mobile bound states of Rydberg excitations in a lattice, Phys. Rev. A 97, 043415 (2018).
  63. S. Wüster, C. Ates, A. Eisfeld, and J. M. Rost, Excitation transport through Rydberg dressing, New J. Phys. 13, 073044 (2011).
  64. A. W. Glaetzle, M. Dalmonte, R. Nath, C. Gross, I. Bloch, and P. Zoller, Designing frustrated quantum magnets with laser-dressed Rydberg atoms, Phys. Rev. Lett. 114, 173002 (2015).
  65. R. M. W. van Bijnen and T. Pohl, Quantum magnetism and topological ordering via Rydberg dressing near Förster resonances, Phys. Rev. Lett. 114, 243002 (2015).
  66. X. X. Li, J. B. You, X. Q. Shao, and W. Li, Coherent ground-state transport of neutral atoms, Phys. Rev. A 105, 032417 (2022).
  67. 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).
  68. 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).
  69. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, et al., SciPy 1.0: Fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).

Outline

Information

Phys. Rev. Research 8, 023260– Published 8 June, 2026
  • Received 23 June 2025
  • Accepted 3 May 2026
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