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Observation of Topological Berry Phases with a Single Phonon in an Ion Microtrap Array

Justin F. Niedermeyer1,2,*, Nathan K. Lysne1,2,†, Katherine C. McCormick1,2, Jonas Keller1,2,‡, Craig W. Hogle3, Matthew G. Blain3, Edwin J. Heller3, Roman Schmied4,§, Robert Jördens1,∥ et al.

Susanna L. Todaro1,2, David J. Wineland1,¶, Andrew C. Wilson1, Daniel H. Slichter1, and Dietrich Leibfried1,**

  • *Contact author: justin.f.niedermeyer@gmail.com
  • †Present address: Quantinuum K.K., Chiyoda-ku, Tokyo, 100-0004, Japan.
  • ‡Present address: Physikalisch-Technische Bundesanstalt, D-38116 Braunschweig, Germany.
  • §Present address: Viewpointsystem GmbH, A-1010 Vienna, Austria.
  • ∥Present address: QUARTIQ GmbH, D-12489 Berlin, Germany.
  • Present address: Department of Physics, University of Oregon, Eugene, Oregon 97403-1274, USA.
  • **Contact author: dietrich.leibfried@nist.gov
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Phys. Rev. X 16, 041037 – Published 10 November, 2026

DOI: https://doi.org/10.1103/td5k-t1mf

Abstract

Controlled quantum mechanical motion of trapped atomic ions can be used to simulate and explore collective quantum phenomena and to process quantum information. Groups of cold atomic ions confined in an externally applied trapping potential self-organize into “Coulomb crystals” due to their mutual electrostatic repulsion. The motion of the ions in these crystals is strongly coupled, and most eigenmodes of motion involve multiple ions. While this enables studies of many-body physics, it limits the flexibility and tunability of the system as a quantum platform. Here, we demonstrate an array of trapped ions in individual trapping sites whose motional modes can be controllably coupled and decoupled by locally tuning the confining potential for each ion. A single motional quantum, or phonon, can be coherently shared among two or three ions located at the vertices of an equilateral triangle 30  μm on a side. We tune the motional eigenmodes about closed contours in configuration space and observe that, if the contour adiabatically encircles a conical intersection present in the motional eigenvalue surfaces, the single-phonon wave function acquires a topological Berry phase that is independent of the contour shape. We characterize these phases by single-phonon interference and study how phase changes occur when the motional mode tuning becomes nonadiabatic. Our results show that precise, individual quantum control of ion motion in a two-dimensional array provides unique access to quantum multibody effects.

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Physics Subject Headings (PhySH)

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While trapped atomic ions are powerful platforms for quantum simulation, relying on naturally organized ion crystals limits the tunability required to fully explore complex quantum phenomena. To overcome this, we trap three individual ions in a two-dimensional triangular microtrap array and coherently share a single quantum of motion, a phonon, among them by locally tuning the electrical potential of each trapping site. By varying the potential energy along closed paths in parameter space that enclose a conical intersection, we directly observe the topological Berry phase acquired by the phonon wave function through interference measurements. This precise control allows us to dynamically manipulate motional modes and verify the path independence of this fundamental topological phase. Ultimately, we expect that programmable spatial structures in microtrap arrays will expand the available toolkit for quantum simulators, providing unique access to quantum many-body effects.

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References (58)

  1. D. Porras and J. I. Cirac, Effective quantum spin systems with trapped ions, Phys. Rev. Lett. 92, 207901 (2004).
  2. D. Porras and J. I. Cirac, Bose-Einstein condensation and strong-correlation behavior of phonons in ion traps, Phys. Rev. Lett. 93, 263602 (2004).
  3. J. I. Cirac and P. Zoller, Quantum computations with cold trapped ions, Phys. Rev. Lett. 74, 4091 (1995).
  4. S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, Al+27 quantum-logic clock with a systematic uncertainty below 10−18, Phys. Rev. Lett. 123, 033201 (2019).
  5. C.-W. Chou, C. Kurz, D. B. Hume, P. N. Plessow, D. R. Leibrandt, and D. Leibfried, Preparation and coherent manipulation of pure quantum states of a single molecular ion, Nature (London) 545, 203 (2017).
  6. P. Micke, T. Leopold, S. A. King, E. Benkler, L. J. Spieß, L. Schmöger, M. Schwarz, J. R. Crespo López-Urrutia, and P. O. Schmidt, Coherent laser spectroscopy of highly charged ions using quantum logic, Nature (London) 578, 60 (2020).
  7. M. G. Raizen, J. M. Gilligan, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Ionic crystals in a linear Paul trap, Phys. Rev. A 45, 6493 (1992).
  8. F. Diedrich, E. Peik, J. M. Chen, W. Quint, and H. Walther, Observation of a phase transition of stored laser-cooled ions, Phys. Rev. Lett. 59, 2931 (1987).
  9. D. J. Wineland, J. C. Bergquist, W. M. Itano, J. J. Bollinger, and C. H. Manney, Atomic-ion Coulomb clusters in an ion trap, Phys. Rev. Lett. 59, 2935 (1987).
  10. S. L. Gilbert, J. J. Bollinger, and D. J. Wineland, Shell-structure phase of magnetically confined strongly coupled plasmas, Phys. Rev. Lett. 60, 2022 (1988).
  11. Y. Wang, M. Qiao, Z. Cai, K. Zhang, N. Jin, P. Wang, W. Chen, C. Luan, B. Du, H. Wang, Y. Song, D. Yum, and K. Kim, Coherently manipulated 2D ion crystal in a monolithic Paul trap, Adv. Quantum Technol. 3, 2000068 (2020).
  12. M. K. Ivory, A. Kato, A. Hasanzadeh, and B. B. Blinov, A Paul trap with sectored ring electrodes for experiments with two-dimensional ion crystals, Rev. Sci. Instrum. 91, 053201 (2020).
  13. Y. Xie, J. Cui, M. D’Onofrio, A. J. Rasmusson, S. W. Howell, and P. Richerme, An open-endcap blade trap for radial-2D ion crystals, Quantum Sci. Technol. 6, 044009 (2021).
  14. D. Kiesenhofer, H. Hainzer, A. Zhdanov, P. C. Holz, M. Bock, T. Ollikainen, and C. F. Roos, Controlling two-dimensional Coulomb crystals of more than 100 ions in a monolithic radio-frequency trap, PRX Quantum 4, 020317 (2023).
  15. S.-A. Guo, Y.-K. Wu, J. Ye, L. Zhang, W.-Q. Lian, R. Yao, Y. Wang, R.-Y. Yan, Y.-J. Yi, Y.-L. Xu, B.-W. Li, Y.-H. Hou, Y.-Z. Xu, W.-X. Guo, C. Zhang, B.-X. Qi, Z.-C. Zhou, L. He, and L.-M. Duan, A site-resolved two-dimensional quantum simulator with hundreds of trapped ions, Nature (London) 630, 613 (2024).
  16. J. W. Britton, B. C. Sawyer, A. C. Keith, C.-C. J. Wang, J. K. Freericks, H. Uys, M. J. Biercuk, and J. J. Bollinger, Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins, Nature (London) 484, 489 (2012).
  17. J. G. Bohnet, B. C. Sawyer, J. W. Britton, M. L. Wall, A. M. Rey, M. Foss-Feig, and J. J. Bollinger, Quantum spin dynamics and entanglement generation with hundreds of trapped ions, Science 352, 1297 (2016).
  18. J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z. X. Gong, and C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator, Nature (London) 551, 601 (2017).
  19. B.-W. Li, Y.-K. Wu, Q.-X. Mei, R. Yao, W.-Q. Lian, M.-L. Cai, Y. Wang, B.-X. Qi, L. Yao, L. He, Z.-C. Zhou, and L.-M. Duan, Probing critical behavior of long-range transverse-field Ising model through quantum Kibble-Zurek Mechanism, PRX Quantum 4, 010302 (2023).
  20. H. Hainzer, D. Kiesenhofer, T. Ollikainen, M. Bock, F. Kranzl, M. K. Joshi, G. Yoeli, R. Blatt, T. Gefen, and C. F. Roos, Correlation spectroscopy with multiqubit-enhanced phase estimation, Phys. Rev. X 14, 011033 (2024).
  21. A. J. Kollár, M. Fitzpatrick, and A. A. Houck, Hyperbolic lattices in circuit quantum electrodynamics, Nature (London) 571, 45 (2019).
  22. J. Chiaverini and W. E. Lybarger, Laserless trapped-ion quantum simulations without spontaneous scattering using microtrap arrays, Phys. Rev. A 77, 022324 (2008).
  23. R. Schmied, J. H. Wesenberg, and D. Leibfried, Optimal surface-electrode trap lattices for quantum simulation with trapped ions, Phys. Rev. Lett. 102, 233002 (2009).
  24. P. C. Holz, S. Auchter, G. Stocker, M. Valentini, K. Lakhmanskiy, C. Rössler, P. Stampfer, S. Sgouridis, E. Aschauer, Y. Colombe, and R. Blatt, 2D linear trap array for quantum information processing, Adv. Quantum Technol. 3, 2000031 (2020).
  25. D. Palani, F. Hasse, P. Kiefer, F. Boeckling, J.-P. Schroeder, U. Warring, and T. Schaetz, High-fidelity transport of trapped-ion qubits in a multilayer array, Phys. Rev. A 107, L050601 (2023).
  26. M. Mielenz, H. Kalis, M. Wittemer, F. Hakelberg, U. Warring, R. Schmied, M. Blain, P. Maunz, D. L. Moehring, D. Leibfried, and T. Schaetz, Arrays of individually controlled ions suitable for two-dimensional quantum simulations, Nat. Commun. 7, ncomms11839 (2016).
  27. F. Hakelberg, P. Kiefer, M. Wittemer, U. Warring, and T. Schaetz, Interference in a prototype of a two-dimensional ion trap array quantum simulator, Phys. Rev. Lett. 123, 100504 (2019).
  28. M. V. Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. A 392, 45 (1984).
  29. J. Larson, E. Sjöqvist, and P. Öhberg, Conical Intersections in Physics (Springer, New York, 2020).
  30. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
  31. W. Domcke and D. R. Yarkony, Role of conical intersections in molecular spectroscopy and photoinduced chemical dynamics, Annu. Rev. Phys. Chem. 63, 325 (2012).
  32. A. K. Geim and K. S. Novoselov, The rise of graphene, Nat. Mater. 6, 183 (2007).
  33. L. Duca, T. Li, M. Reitter, I. Bloch, M. Schleier-Smith, and U. Schneider, An Aharonov-Bohm interferometer for determining Bloch band topology, Science 347, 288 (2015).
  34. C. S. Wang, N. E. Frattini, B. J. Chapman, S. Puri, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, Observation of wave-packet branching through an engineered conical intersection, Phys. Rev. X 13, 011008 (2023).
  35. C. H. Valahu, V. C. Olaya-Agudelo, R. J. MacDonell, T. Navickas, A. D. Rao, M. J. Millican, J. B. Pérez-Sánchez, J. Yuen-Zhou, M. J. Biercuk, C. Hempel, T. R. Tan, and I. Kassal, Direct observation of geometric-phase interference in dynamics around a conical intersection, Nat. Chem. 15, 1503 (2023).
  36. J. Whitlow, Z. Jia, Y. Wang, C. Fang, J. Kim, and K. R. Brown, Quantum simulation of conical intersections using trapped ions, Nat. Chem. 15, 1509 (2023).
  37. N. K. Lysne, J. F. Niedermeyer, A. C. Wilson, D. H. Slichter, and D. Leibfried, Individual addressing and state readout of trapped ions utilizing radio-frequency micromotion, Phys. Rev. Lett. 133, 033201 (2024).
  38. J. F. Niedermeyer, Quantum control in a two-dimensional ion microtrap array, Ph.D. thesis, University of Colorado Boulder, Colorado, United States, 2025.
  39. P. L. W. Maunz, High Optical Access Trap 2.0., Technical Report, SAND-2016-0796R (Sandia National Lab. (SNL-NM), Albuquerque, NM (United States), 2016).
  40. D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Minimization of ion micromotion in a Paul trap, J. Appl. Phys. 15, 5025 (1998).
  41. D. J. Wineland, C. Monroe, W. M. Itano, D. G. Leibfried, B. E. King, and D. M. Meekhof, Experimental issues in coherent quantum-state manipulation of trapped atomic ions, J. Res. Natl. Inst. Stand. Technol. 103, 259 (1998).
  42. C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Resolved-sideband Raman cooling of a bound atom to the 3D zero-point energy, Phys. Rev. Lett. 75, 4011 (1995).
  43. S. L. Todaro, Scalable state detection and fast transport of trapped-ion qubits for quantum computing, Ph.D. thesis, University of Colorado Boulder, Colorado, United States, 2020.
  44. K. C. McCormick, J. Keller, D. J. Wineland, A. C. Wilson, and D. Leibfried, Coherently displaced oscillator quantum states of a single trapped atom, Quantum Sci. Technol. 4, 024010 (2019).
  45. K. R. Brown, C. Ospelkaus, Y. Colombe, A. C. Wilson, D. Leibfried, and D. J. Wineland, Coupled quantized mechanical oscillators, Nature (London) 471, 196 (2011).
  46. M. Harlander, R. Lechner, M. Brownnutt, R. Blatt, and W. Hänsel, Trapped-ion antennae for the transmission of quantum information, Nature (London) 471, 200 (2011).
  47. A. C. Wilson, Y. Colombe, K. R. Brown, E. Knill, D. Leibfried, and D. J. Wineland, Tunable spin–spin interactions and entanglement of ions in separate potential wells, Nature (London) 512, 57 (2014).
  48. M. Qiao, Z. Cai, Y. Wang, B. Du, N. Jin, W. Chen, P. Wang, C. Luan, E. Gao, X. Sun, H. Tian, J. Zhang, and K. Kim, Tunable quantum simulation of spin models with a two-dimensional ion crystal, Nat. Phys. 20, 623 (2024).
  49. M. Foss-Feig, G. Pagano, A. C. Potter, and N. Y. Yao, Progress in trapped-ion quantum simulation, Annu. Rev. Condens. Matter Phys. 16, 145 (2025).
  50. U. Warring, F. Hakelberg, P. Kiefer, M. Wittemer, and T. Schaetz, Trapped ion architecture for multi-dimensional quantum simulations, Adv. Quantum Technol. 3, 1900137 (2020).
  51. K. K. Mehta, C. Zhang, M. Malinowski, T.-L. Nguyen, M. Stadler, and J. P. Home, Integrated optical multi-ion quantum logic, Nature (London) 586, 533 (2020).
  52. R. J. Niffenegger, J. Stuart, C. Sorace-Agaskar, D. Kharas, S. Bramhavar, C. D. Bruzewicz, W. Loh, R. T. Maxson, R. McConnell, D. Reens, G. N. West, J. M. Sage, and J. Chiaverini, Integrated multi-wavelength control of an ion qubit, Nature (London) 586, 538 (2020).
  53. R. Schmied, J. H. Wesenberg, and D. Leibfried, Quantum simulation of the hexagonal Kitaev model with trapped ions, New J. Phys. 13, 115011 (2011).
  54. A. Ransford et al., A 98-qubit trapped-ion quantum computer with all-to-all connectivity, Nature (London) 655, 81 (2026).
  55. A. Bermudez, T. Schaetz, and D. Porras, Synthetic gauge fields for vibrational excitations of trapped ions, Phys. Rev. Lett. 107, 150501 (2011).
  56. S. Aaronson and A. Arkhipov, The computational complexity of linear optics, Theory Comput. 9, 143 (2013).
  57. Q.-X. Mei, B.-W. Li, Y.-K. Wu, M.-L. Cai, Y. Wang, L. Yao, Z.-C. Zhou, and L.-M. Duan, Experimental realization of the Rabi-Hubbard model with trapped ions, Phys. Rev. Lett. 128, 160504 (2022).
  58. B.-W. Li, Q.-X. Mei, K. Wu, M.-L. Cai, Y. Wang, L. Yao, Z.-C. Zhou, and L.-M. Duan, Observation of non-Markovian spin dynamics in a Jaynes-Cummings-Hubbard model using a trapped-ion quantum simulator, Phys. Rev. Lett. 129, 140501 (2022).

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Phys. Rev. X 16, 041037– Published 10 November, 2026
  • Received 31 March 2026
  • Accepted 2 October 2026
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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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