- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

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
  • Editors' Suggestion
  • Open Access

Partial Landau-Zener transitions and applications to qubit shuttling

Jonas R. F. Lima and Guido Burkard

PDF

Phys. Rev. B 111, 235439 – Published 20 June, 2025

DOI: https://doi.org/10.1103/y4xf-zjjx

Abstract

The transition dynamics of two-state systems with time-dependent energy levels, first considered by Landau, Zener, Majorana, and Stückelberg, is one of the basic models in quantum physics and has been used to describe various physical systems. We propose here a generalization of the Landau-Zener (LZ) problem characterized by distinct paths of the instantaneous eigenstates as the system evolves in time while keeping the instantaneous eigenenergies exactly as in the standard LZ model. We show that these paths play an essential role in the transition probability P between the two states, and can lead to a substantial reduction of P, being possible even to achieve P=0 in an instructive extreme case, and also to large P even in the absence of any anticrossing point. The partial LZ model can describe valley transition dynamics during charge and spin shuttling in semiconductor quantum dots.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (60)

  1. L. D. Landau, On the theory of transfer of energy at collisions II, Phys. Z. Sowjetunion 2, 42 (1932).
  2. C. Zener, Non-adiabatic crossing of energy levels, Proc. R. Soc. A 137, 696 (1932).
  3. E. C. G. Stückelberg, Theorie der unelastischen Stösse zwischen Atomen, Helv. Phys. Acta 5, 369 (1932).
  4. E. Majorana, Atomi orientati in campo magnetico variabile, Nuovo Cimento 9, 43 (1932).
  5. O. V. Ivakhnenko, S. N. Shevchenko, and F. Nori, Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference, Phys. Rep. 995, 1 (2023).
  6. T. Higuchi, C. Heide, K. Ullmann, H. B. Weber, and P. Hommelhoff, Light-field-driven currents in graphene, Nature (London) 550, 224 (2017).
  7. M. Mark, T. Kraemer, P. Waldburger, J. Herbig, C. Chin, H.-C. Nägerl, and R. Grimm, “Stückelberg interferometry” with ultracold molecules, Phys. Rev. Lett. 99, 113201 (2007).
  8. J. R. Petta, H. Lu, and A. C. Gossard, A coherent beam splitter for electronic spin states, Science 327, 669 (2010).
  9. H. Ribeiro, G. Burkard, J. R. Petta, H. Lu, and A. C. Gossard, Coherent adiabatic spin control in the presence of charge noise using tailored pulses, Phys. Rev. Lett. 110, 086804 (2013).
  10. G. Cao, H.-O. Li, T. Tu, L. Wang, C. Zhou, M. Xiao, G.-C. Guo, H.-W. Jiang, and G.-P. Guo, Ultrafast universal quantum control of a quantum-dot charge qubit using Landau-Zener-Stückelberg interference, Nat. Commun. 4, 1401 (2013).
  11. T. Faust, J. Rieger, M. J. Seitner, P. Krenn, J. P. Kotthaus, and E. M. Weig, Nonadiabatic dynamics of two strongly coupled nanomechanical resonator modes, Phys. Rev. Lett. 109, 037205 (2012).
  12. E. Dupont-Ferrier, B. Roche, B. Voisin, X. Jehl, R. Wacquez, M. Vinet, M. Sanquer, and S. De Franceschi, Coherent coupling of two dopants in a silicon nanowire probed by Landau-Zener-Stückelberg interferometry, Phys. Rev. Lett. 110, 136802 (2013).
  13. A. Izmalkov, M. Grajcar, E. Il'ichev, N. Oukhanski, T. Wagner, H.-G. Meyer, W. Krech, M. H. S. Amin, A. M. van den Brink, and A. M. Zagoskin, Observation of macroscopic Landau-Zener transitions in a superconducting device, Europhys. Lett. 65, 844 (2004).
  14. K. Pyka, J. Keller, H. L. Partner, R. Nigmatullin, T. Burgermeister, D. M. Meier, K. Kuhlmann, A. Retzker, M. B. Plenio, W. H. Zurek, A. del Campo, and T. E. Mehlstäubler, Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals, Nat. Commun. 4, 2291 (2013).
  15. J. R. F. Lima and G. Burkard, Interface and electromagnetic effects in the valley splitting of Si quantum dots, Mater. Quantum Technol. 3, 025004 (2023).
  16. J. R. F. Lima and G. Burkard, Valley splitting depending on the size and location of a silicon quantum dot, Phys. Rev. Mater. 8, 036202 (2024).
  17. T. Fujita, T. A. Baart, C. Reichl, W. Wegscheider, and L. M. K. Vandersypen, Coherent shuttle of electron-spin states, npj Quantum Inf. 3, 22 (2017).
  18. A. Mills, D. Zajac, M. Gullans, F. Schupp, T. Hazard, and J. Petta, Shuttling a single charge across a one-dimensional array of silicon quantum dots, Nat. Commun. 10, 1063 (2019).
  19. B. Jadot, P.-A. Mortemousque, E. Chanrion, V. Thiney, A. Ludwig, A. D. Wieck, M. Urdampilleta, C. Bäuerle, and T. Meunier, Distant spin entanglement via fast and coherent electron shuttling, Nat. Nanotechnol. 16, 570 (2021).
  20. A. Noiri, K. Takeda, T. Nakajima, T. Kobayashi, A. Sammak, G. Scappucci, and S. Tarucha, A shuttling-based two-qubit logic gate for linking distant silicon quantum processors, Nat. Commun. 13, 5740 (2022).
  21. A. M. J. Zwerver, S. V. Amitonov, S. L. de Snoo, M. T. Madzik, M. Rimbach-Russ, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Shuttling an electron spin through a silicon quantum dot array, PRX Quantum 4, 030303 (2023).
  22. F. van Riggelen-Doelman, C.-A. Wang, S. L. de Snoo, W. I. Lawrie, N. W. Hendrickx, M. Rimbach-Russ, A. Sammak, G. Scappucci, C. Déprez, and M. Veldhorst, Coherent spin qubit shuttling through germanium quantum dots, Nat. Commun. 15, 5716 (2024).
  23. T. Struck, M. Volmer, L. Visser, T. Offermann, R. Xue, J.-S. Tu, S. Trellenkamp, Ł. Cywiński, H. Bluhm, and L. R. Schreiber, Spin-EPR-pair separation by conveyor-mode single electron shuttling in Si/SiGe, Nat. Commun. 15, 1325 (2024).
  24. M. D. Smet, Y. Matsumoto, A.-M. J. Zwerver, L. Tryputen, S. L. de Snoo, S. V. Amitonov, S. R. Katiraee-Far, A. Sammak, N. Samkharadze, Ö. Gül, R. N. M. Wasserman, E. Greplová, M. Rimbach-Russ, G. Scappucci, and L. M. K. Vandersypen, High-fidelity single-spin shuttling in silicon, Nat. Nanotechnol. (2025), doi:10.1038/s41565-025-01920-5.
  25. F. Ginzel, A. R. Mills, J. R. Petta, and G. Burkard, Spin shuttling in a silicon double quantum dot, Phys. Rev. B 102, 195418 (2020).
  26. V. Langrock, J. A. Krzywda, N. Focke, I. Seidler, L. R. Schreiber, and L. Cywiński, Blueprint of a scalable spin qubit shuttle device for coherent mid-range qubit transfer in disordered Si/SiGe/SiO2, PRX Quantum 4, 020305 (2023).
  27. S. Bosco, J. Zou, and D. Loss, High-fidelity spin qubit shuttling via large spin-orbit interactions, PRX Quantum 5, 020353 (2024).
  28. M. P. Losert, M. Oberländer, J. D. Teske, M. Volmer, L. R. Schreiber, H. Bluhm, S. N. Coppersmith, and M. Friesen, Strategies for enhancing spin-shuttling fidelities in Si/SiGe quantum wells with random-alloy disorder, PRX Quantum 5, 040322 (2024).
  29. M. Volmer, T. Struck, A. Sala, B. Chen, M. Oberländer, T. Offermann, R. Xue, L. Visser, J.-S. Tu, S. Trellenkamp, Ł. Cywiński, H. Bluhm, and L. R. Schreiber, Mapping of valley splitting by conveyor-mode spin-coherent electron shuttling, npj Quantum Inf. 10, 61 (2024).
  30. N. V. Vitanov and B. M. Garraway, Landau-Zener model: Effects of finite coupling duration, Phys. Rev. A 53, 4288 (1996).
  31. S. Shevchenko, S. Ashhab, and F. Nori, Landau-Zener-Stückelberg interferometry, Phys. Rep. 492, 1 (2010).
  32. S. Ashhab, O. A. Ilinskaya, and S. N. Shevchenko, Nonlinear Landau-Zener-Stückelberg-Majorana problem, Phys. Rev. A 106, 062613 (2022).
  33. N. V. Vitanov and K.-A. Suominen, Nonlinear level-crossing models, Phys. Rev. A 59, 4580 (1999).
  34. N. Rosen and C. Zener, Double Stern-Gerlach experiment and related collision phenomena, Phys. Rev. 40, 502 (1932).
  35. F. T. Hioe, Solution of Bloch equations involving amplitude and frequency modulations, Phys. Rev. A 30, 2100 (1984).
  36. K.-A. Suominen and B. M. Garraway, Population transfer in a level-crossing model with two time scales, Phys. Rev. A 45, 374 (1992).
  37. J. M. S. Lehto and K.-A. Suominen, Time-dependent two-level models and zero-area pulses, Phys. Scr. 91, 013005 (2016).
  38. V. L. Pokrovsky and N. A. Sinitsyn, Landau-Zener transitions in a linear chain, Phys. Rev. B 65, 153105 (2002).
  39. V. L. Pokrovsky and N. A. Sinitsyn, Spin transitions in time-dependent regular and random magnetic fields, Phys. Rev. B 69, 104414 (2004).
  40. A. V. Shytov, Landau-Zener transitions in a multilevel system: An exact result, Phys. Rev. A 70, 052708 (2004).
  41. D. A. Garanin, R. Neb, and R. Schilling, Effect of environmental spins on Landau-Zener transitions, Phys. Rev. B 78, 094405 (2008).
  42. A. Altland and V. Gurarie, Many body generalization of the Landau-Zener problem, Phys. Rev. Lett. 100, 063602 (2008).
  43. A. M. Dykhne, Quantum transitions in the adiabatic approximation, Sov. Phys. JETP 11, 411 (1960).
  44. A. M. Dykhne, Adiabatic perturbation of discrete spectrum states, Sov. Phys. JETP 14, 941 (1962).
  45. J. P. Davis and P. Pechukas, Nonadiabatic transitions induced by a time-dependent Hamiltonian in the semiclassical/adiabatic limit: The two-state case, J. Chem. Phys. 64, 3129 (1976).
  46. M. V. Berry, Geometric amplitude factors in adiabatic quantum transitions, Proc. R. Soc. London, Ser. A 430, 405 (1990).
  47. M. Born and V. A. Fock, Beweis des adiabatensatzes, Z. Phys. 51, 165 (1928).
  48. D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, Shortcuts to adiabaticity: Concepts, methods, and applications, Rev. Mod. Phys. 91, 045001 (2019).
  49. Y. N. Demkov and M. Kunike, Hypergeometric models of the two-state approximation in the theory of atomic collisions, Vestn. Leningr. Univ. Fis. Khim. 16, 39 (1969).
  50. R. Requist, J. Schliemann, A. G. Abanov, and D. Loss, Double occupancy errors in quantum computing operations: Corrections to adiabaticity, Phys. Rev. B 71, 115315 (2005).
  51. M. Wubs, K. Saito, S. Kohler, P. Hänggi, and Y. Kayanuma, Gauging a quantum heat bath with dissipative Landau-Zener transitions, Phys. Rev. Lett. 97, 200404 (2006).
  52. K. Saito, M. Wubs, S. Kohler, Y. Kayanuma, and P. Hänggi, Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior, Phys. Rev. B 75, 214308 (2007).
  53. P. Nalbach and M. Thorwart, Landau-Zener transitions in a dissipative environment: Numerically exact results, Phys. Rev. Lett. 103, 220401 (2009).
  54. Z. Huang and Y. Zhao, Dynamics of dissipative Landau-Zener transitions, Phys. Rev. A 97, 013803 (2018).
  55. F. Zheng, Y. Shen, K. Sun, and Y. Zhao, Photon-assisted Landau-Zener transitions in a periodically driven Rabi dimer coupled to a dissipative mode, J. Chem. Phys. 154, 044102 (2021).
  56. R. Dann, A. Tobalina, and R. Kosloff, Fast route to equilibration, Phys. Rev. A 101, 052102 (2020).
  57. R. Dann and R. Kosloff, Inertial theorem: Overcoming the quantum adiabatic limit, Phys. Rev. Res. 3, 013064 (2021).
  58. M. Friesen, S. Chutia, C. Tahan, and S. N. Coppersmith, Valley splitting theory of SiGe/Si/SiGe quantum wells, Phys. Rev. B 75, 115318 (2007).
  59. A. L. Saraiva, M. J. Calderón, R. B. Capaz, X. Hu, S. Das Sarma, and B. Koiller, Intervalley coupling for interface-bound electrons in silicon: An effective mass study, Phys. Rev. B 84, 155320 (2011).
  60. A. Hosseinkhani and G. Burkard, Electromagnetic control of valley splitting in ideal and disordered Si quantum dots, Phys. Rev. Res. 2, 043180 (2020).

Outline

Information

Phys. Rev. B 111, 235439– Published 20 June, 2025
  • Received 6 August 2024
  • Revised 11 November 2024
  • Accepted 16 April 2025
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