- 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
  • Open Access

Coupling-energy driven pumping through quantum dots: Role of coherences

Lukas Litzba1,*, Gernot Schaller2, Jürgen König1, and Nikodem Szpak1,†

  • *Contact author: lukas.litzba@uni-due.de
  • †Contact author: nikodem.szpak@uni-due.de
PDF

Phys. Rev. B 113, 235152 – Published 25 June, 2026

DOI: https://doi.org/10.1103/m2jb-z9lm

Abstract

We study the impact of off-resonant tunneling and coherences on the electron pumping through quantum dots. Thereby, we focus on two electron-pump setups where lowest-order tunneling processes are suppressed and the pump is exclusively driven by modulations of the coupling energy. The first setup is driven by switching on and off the couplings between the quantum dot and the leads, while the second setup employs measurements of the dot occupation. We derive exact solutions for arbitrarily strong tunnel couplings in the absence of Coulomb interaction, identify parameter regimes with optimal pumping currents or optimal energy efficiency, and discuss similarities between both pumping mechanisms.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (89)

  1. D. Newman, F. Mintert, and A. Nazir, Performance of a quantum heat engine at strong reservoir coupling, Phys. Rev. E 95, 032139 (2017).
  2. M. Wiedmann, J. T. Stockburger, and J. Ankerhold, Non-Markovian dynamics of a quantum heat engine: Out-of-equilibrium operation and thermal coupling control, New J. Phys. 22, 033007 (2020).
  3. P. A. Camati, J. F. G. Santos, and R. M. Serra, Employing non-Markovian effects to improve the performance of a quantum Otto refrigerator, Phys. Rev. A 102, 012217 (2020).
  4. Y. Shirai, K. Hashimoto, R. Tezuka, C. Uchiyama, and N. Hatano, Non-Markovian effect on quantum Otto engine: Role of system-reservoir interaction, Phys. Rev. Res. 3, 023078 (2021).
  5. M. Ishizaki, N. Hatano, and H. Tajima, Switching the function of the quantum Otto cycle in non-Markovian dynamics: Heat engine, heater, and heat pump, Phys. Rev. Res. 5, 023066 (2023).
  6. A. Das and V. Mukherjee, Quantum-enhanced finite-time Otto cycle, Phys. Rev. Res. 2, 033083 (2020).
  7. V. Mukherjee, A. G. Kofman, and G. Kurizki, Anti-Zeno quantum advantage in fast-driven heat machines, Commun. Phys. 3, 8 (2020).
  8. M. Xu, J. Stockburger, G. Kurizki, and J. Ankerhold, Minimal quantum thermal machine in a bandgap environment: Non-Markovian features and anti-Zeno advantage, New J. Phys. 24, 035003 (2022).
  9. K. Ptaszyński, Non-Markovian thermal operations boosting the performance of quantum heat engines, Phys. Rev. E 106, 014114 (2022).
  10. I. A. Picatoste, A. Colla, and H.-P. Breuer, Dynamically emergent quantum thermodynamics: Non-Markovian Otto cycle, Phys. Rev. Res. 6, 013258 (2024).
  11. J. Liu, K. A. Jung, and D. Segal, Periodically driven quantum thermal machines from warming up to limit cycle, Phys. Rev. Lett. 127, 200602 (2021).
  12. C. L. Latune, G. Pleasance, and F. Petruccione, Cyclic quantum engines enhanced by strong bath coupling, Phys. Rev. Appl. 20, 024038 (2023).
  13. S. P. Katoorani, C. Kohlfürst, F. Queisser, G. Schaller, and R. Schützhold, Finite-time performance of a cyclic two-dimensional quantum Ising heat engine, Phys. Rev. E 112, 014122 (2025).
  14. S. Gatto, A. Colla, H.-P. Breuer, and M. Thoss, Quantum Otto cycle in the Anderson impurity model, arXiv:2601.21546 [cond-mat].
  15. A. Ghosh, V. Mukherjee, W. Niedenzu, and G. Kurizki, Are quantum thermodynamic machines better than their classical counterparts? Eur. Phys. J. 227, 2043 (2019).
  16. S. Restrepo, S. Böhling, J. Cerrillo, and G. Schaller, Electron pumping in the strong coupling and non-Markovian regime: A reaction coordinate mapping approach, Phys. Rev. B 100, 035109 (2019).
  17. A. A. S. Kalaee, A. Wacker, and P. P. Potts, Violating the thermodynamic uncertainty relation in the three-level maser, Phys. Rev. E 104, L012103 (2021).
  18. F. Cavaliere, M. Carrega, G. De Filippis, V. Cataudella, G. Benenti, and M. Sassetti, Dynamical heat engines with non-Markovian reservoirs, Phys. Rev. Res. 4, 033233 (2022).
  19. M. Alamo, F. Petiziol, and A. Eckardt, Minimal quantum heat pump based on high-frequency driving and non-Markovianity, Phys. Rev. E 109, 064121 (2024).
  20. L. M. Cangemi, C. Bhadra, and A. Levy, Quantum engines and refrigerators, Phys. Rep. 1087, 1 (2024).
  21. L. S. Schulman and B. Gaveau, Ratcheting up energy by means of measurement, Phys. Rev. Lett. 97, 240405 (2006).
  22. N. Erez, G. Gordon, M. Nest, and G. Kurizki, Thermodynamic control by frequent quantum measurements, Nature 452, 724 (2008).
  23. M. Esposito, K. Lindenberg, and C. Van den Broeck, Entropy production as correlation between system and reservoir, New J. Phys. 12, 013013 (2010).
  24. M. Esposito, M. A. Ochoa, and M. Galperin, Nature of heat in strongly coupled open quantum systems, Phys. Rev. B 92, 235440 (2015).
  25. P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Quantum and information thermodynamics: A unifying framework based on repeated interactions, Phys. Rev. X 7, 021003 (2017).
  26. P. Strasberg and M. Esposito, Non-Markovianity and negative entropy production rates, Phys. Rev. E 99, 012120 (2019).
  27. A. Trushechkin, M. Merkli, J. Cresser, and J. Anders, Open quantum system dynamics and the mean force Gibbs state, AVS Quantum Sci. 4, 012301 (2022).
  28. L. Litzba, E. Kleinherbers, J. König, R. Schützhold, and N. Szpak, Effective time-dependent temperature for fermionic master equations beyond the Markov and the secular approximations, Phys. Rev. B 111, 085103 (2025).
  29. I. A. Picatoste, A. Colla, and H.-P. Breuer, Local and global approaches to the thermodynamics of pure decoherence processes in open quantum systems, Phys. Rev. A 112, 022210 (2025).
  30. A. Colla, B. Vacchini, and A. Smirne, Local energy assignment for two interacting quantum thermal reservoirs, New J. Phys. 27, 124510 (2025).
  31. M. Perarnau-Llobet, H. Wilming, A. Riera, R. Gallego, and J. Eisert, Strong coupling corrections in quantum thermodynamics, Phys. Rev. Lett. 120, 120602 (2018).
  32. D. Gelbwaser-Klimovsky, N. Erez, R. Alicki, and G. Kurizki, Work extraction via quantum nondemolition measurements of qubits in cavities: Non-Markovian effects, Phys. Rev. A 88, 022112 (2013).
  33. P. Strasberg, G. Schaller, N. Lambert, and T. Brandes, Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping, New J. Phys. 18, 073007 (2016).
  34. G. Engelhardt and G. Schaller, Maxwell's demon in the quantum-Zeno regime and beyond, New J. Phys. 20, 023011 (2018).
  35. G. Schaller, J. Cerrillo, G. Engelhardt, and P. Strasberg, Electronic Maxwell demon in the coherent strong-coupling regime, Phys. Rev. B 97, 195104 (2018).
  36. C. Elouard, S. K. Manikandan, A. N. Jordan, and G. Haack, Revealing the fuel of a quantum continuous measurement-based refrigerator, Phys. Rev. E 113, 014134 (2026).
  37. K. Liu, M. Nakagawa, and M. Ueda, Maxwell's demon for quantum transport, Phys. Rev. A 113, 022436 (2026).
  38. R. A. Bustos-Marún and H. L. Calvo, Thermodynamics and steady state of quantum motors and pumps far from equilibrium, Entropy 21, 824 (2019).
  39. K. Korzekwa, M. Lostaglio, J. Oppenheim, and D. Jennings, The extraction of work from quantum coherence, New J. Phys. 18, 023045 (2016).
  40. W. Chen, S.-W. Han, X. Feng, and J. Feng, Work extraction from long-lived quantum coherence of a three-level system, arXiv:2508.02614 [quant-ph].
  41. A. Kofman and G. Kurizki, Acceleration of quantum decay processes by frequent observations, Nature 405, 546 (2000).
  42. P. Facchi, H. Nakazato, and S. Pascazio, From the quantum Zeno to the inverse quantum Zeno effect, Phys. Rev. Lett. 86, 2699 (2001).
  43. K. Fujii and K. Yamamoto, Anti-Zeno effect for quantum transport in disordered systems, Phys. Rev. A 82, 042109 (2010).
  44. N. Ahmadiniaz, M. Geller, J. König, P. Kratzer, A. Lorke, G. Schaller, and R. Schützhold, Quantum Zeno manipulation of quantum dots, Phys. Rev. Res. 4, L032045 (2022).
  45. M. Switkes, C. M. Marcus, K. Campman, and A. C. Gossard, An adiabatic quantum electron pump, Science 283, 1905 (1999).
  46. Y. Ono and Y. Takahashi, Electron pump by a combined single-electron/field-effect- transistor structure, Appl. Phys. Lett. 82, 1221 (2003).
  47. M. D. Blumenthal, B. Kaestner, L. Li, S. Giblin, T. J. B. M. Janssen, M. Pepper, D. Anderson, G. Jones, and D. A. Ritchie, Gigahertz quantized charge pumping, Nat. Phys. 3, 343 (2007).
  48. B. Kaestner, V. Kashcheyevs, S. Amakawa, M. D. Blumenthal, L. Li, T. J. B. M. Janssen, G. Hein, K. Pierz, T. Weimann, U. Siegner, and H. W. Schumacher, Single-parameter nonadiabatic quantized charge pumping, Phys. Rev. B 77, 153301 (2008).
  49. S. P. Giblin, M. Kataoka, J. D. Fletcher, P. See, T. J. B. M. Janssen, J. P. Griffiths, G. A. C. Jones, I. Farrer, and D. A. Ritchie, Towards a quantum representation of the ampere using single electron pumps, Nat. Commun. 3, 930 (2012).
  50. L. Fricke, M. Wulf, B. Kaestner, F. Hohls, P. Mirovsky, B. Mackrodt, R. Dolata, T. Weimann, K. Pierz, U. Siegner, and H. W. Schumacher, Self-referenced single-electron quantized current source, Phys. Rev. Lett. 112, 226803 (2014).
  51. A. Rossi, T. Tanttu, K. Y. Tan, I. Iisakka, R. Zhao, K. W. Chan, G. C. Tettamanzi, S. Rogge, A. S. Dzurak, and M. Möttönen, An accurate single-electron pump based on a highly tunable silicon quantum dot, Nano Lett. 14, 3405 (2014).
  52. G. Yamahata, K. Nishiguchi, and A. Fujiwara, Gigahertz single-trap electron pumps in silicon, Nat. Commun. 5, 5038 (2014).
  53. B. Kaestner and V. Kashcheyevs, Non-adiabatic quantized charge pumping with tunable-barrier quantum dots: A review of current progress, Rep. Prog. Phys. 78, 103901 (2015).
  54. F. Stein, D. Drung, L. Fricke, H. Scherer, F. Hohls, C. Leicht, M. Götz, C. Krause, R. Behr, E. Pesel, K. Pierz, U. Siegner, F. J. Ahlers, and H. W. Schumacher, Validation of a quantized-current source with 0.2 ppm uncertainty, Appl. Phys. Lett. 107, 103501 (2015).
  55. F. Stein, H. Scherer, T. Gerster, R. Behr, M. Götz, E. Pesel, C. Leicht, N. Ubbelohde, T. Weimann, K. Pierz, H. W. Schumacher, and F. Hohls, Robustness of single-electron pumps at sub-ppm current accuracy level, Metrologia 54, S1 (2017).
  56. J. van der Heijden, G. C. Tettamanzi, and S. Rogge, Dynamics of a single-atom electron pump, Sci. Rep. 7, 44371 (2017).
  57. H. Scherer and H. W. Schumacher, Single-electron pumps and quantum current metrology in the revised SI, Ann. Phys. 531, 1800371 (2019).
  58. S. P. Giblin, A. Fujiwara, G. Yamahata, M.-H. Bae, N. Kim, A. Rossi, M. Möttönen, and M. Kataoka, Evidence for universality of tunable-barrier electron pumps, Metrologia 56, 044004 (2019).
  59. A. Rossi, N. W. Hendrickx, A. Sammak, M. Veldhorst, G. Scappucci, and M. Kataoka, Single-hole pump in germanium, J. Phys. D: Appl. Phys. 54, 434001 (2021).
  60. F. Hohls, V. Kashcheyevs, F. Stein, T. Wenz, B. Kaestner, and H. W. Schumacher, Controlling the error mechanism in a tunable-barrier nonadiabatic charge pump by dynamic gate compensation, Phys. Rev. B 105, 205425 (2022).
  61. A. Dash, S. Yianni, M. K. Feng, F. Hudson, A. Saraiva, A. S. Dzurak, and T. Tanttu, Silicon-charge-pump operation limit above and below liquid-helium temperature, Phys. Rev. Appl. 21, 014040 (2024).
  62. A.-P. Jauho, N. S. Wingreen, and Y. Meir, Time-dependent transport in interacting and noninteracting resonant-tunneling systems, Phys. Rev. B 50, 5528 (1994).
  63. J. Splettstoesser, M. Governale, J. König, and R. Fazio, Adiabatic pumping through a quantum dot with Coulomb interactions: A perturbation expansion in the tunnel coupling, Phys. Rev. B 74, 085305 (2006).
  64. A. Croy and U. Saalmann, Nonadiabatic rectification and current reversal in electron pumps, Phys. Rev. B 86, 035330 (2012).
  65. R.-P. Riwar, J. Splettstoesser, and J. König, Zero-frequency noise in adiabatically driven interacting quantum systems, Phys. Rev. B 87, 195407 (2013).
  66. S. Gurvitz, Single-electron approach for time-dependent electron transport, Phys. Scr. 2015, 014013 (2015).
  67. R. Hussein and S. Kohler, Capacitively coupled nano conductors: Ratchet currents and exchange fluctuation relations, Ann. Phys. 527, 610 (2015).
  68. R. Hussein, S. Kohler, and F. Sols, Heat pump driven by the shot noise of a tunnel contact, Physica E 77, 156 (2016).
  69. A. Croy and U. Saalmann, Full counting statistics of a nonadiabatic electron pump, Phys. Rev. B 93, 165428 (2016).
  70. J. S. Lim, D. Sánchez, and R. López, Engineering drag currents in Coulomb coupled quantum dots, New J. Phys. 20, 023038 (2018).
  71. E. Potanina, K. Brandner, and C. Flindt, Optimization of quantized charge pumping using full counting statistics, Phys. Rev. B 99, 035437 (2019).
  72. S. Gurvitz, Generalized Landauer formula for time-dependent potentials and noise-induced zero-bias dc current, J. Phys. A: Math. Theor. 52, 175301 (2019).
  73. B. Annby-Andersson, D. Bhattacharyya, P. Bakhshinezhad, D. Holst, G. De Sousa, C. Jarzynski, P. Samuelsson, and P. P. Potts, Maxwell's demon across the quantum-to-classical transition, Phys. Rev. Res. 6, 043216 (2024).
  74. R. Sánchez, A. N. Singh, A. N. Jordan, and B. Bhandari, Making the virtual real: Measurement-powered tunneling engines, Phys. Rev. B 113, 125414 (2026).
  75. A. N. Singh, R. Sánchez, and A. N. Jordan, Collective charge measurement in quantum dot chains: Controlling barrier occupation and tunneling current, arXiv:2605.19001 [cond-mat.mes-hall].
  76. É. Jussiau, L. Bresque, A. Auffèves, K. W. Murch, and A. N. Jordan, Many-body quantum vacuum fluctuation engines, Phys. Rev. Res. 5, 033122 (2023).
  77. P. Zedler, G. Schaller, G. Kiesslich, C. Emary, and T. Brandes, Weak-coupling approximations in non-Markovian transport, Phys. Rev. B 80, 045309 (2009).
  78. G. E. Topp, T. Brandes, and G. Schaller, Steady-state thermodynamics of non-interacting transport beyond weak coupling, Europhys. Lett. 110, 67003 (2015).
  79. P. Strasberg, G. Schaller, T. L. Schmidt, and M. Esposito, Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strong-coupling regime, Phys. Rev. B 97, 205405 (2018).
  80. H.-P. Breuer, Foundations and measures of quantum non-Markovianity, J. Phys. B 45, 154001 (2012).
  81. G. Nenciu, Independent electron model for open quantum systems: Landauer-Büttiker formula and strict positivity of the entropy production, J. Math. Phys. 48, 033302 (2007).
  82. B. Misra and E. G. Sudarshan, The Zeno's paradox in quantum theory, J. Math. Phys. 18, 756 (1977).
  83. Y. Guryanova, N. Friis, and M. Huber, Ideal projective measurements have infinite resource costs, Quantum 4, 222 (2020).
  84. R. J. Schoelkopf, P. Wahlgren, A. A. Kozhevnikov, P. Delsing, and D. E. Prober, The radio-frequency single-electron transistor (RF-SET): A fast and ultrasensitive electrometer, Science 280, 1238 (1998).
  85. C. Barthel, M. Kjærgaard, J. Medford, M. Stopa, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Fast sensing of double-dot charge arrangement and spin state with a radio-frequency sensor quantum dot, Phys. Rev. B 81, 161308(R) (2010).
  86. D. Bischoff, M. Eich, O. Zilberberg, C. Rössler, T. Ihn, and K. Ensslin, Measurement back-action in stacked graphene quantum dots, Nano Lett. 15, 6003 (2015).
  87. L. Litzba, Data from the figures in the article “Coupling-energy driven pumping through quantum dots: The role of coherences”, 2026, https://doi.org/10.71955/DUEDATA-2026-18LQAK.
  88. A. G. Redfield, On the theory of relaxation processes, IBM J. Res. Dev. 1, 19 (1957).
  89. N. Szpak, G. Schaller, R. Schützhold, and J. König, Relaxation to persistent currents in a Hubbard trimer coupled to fermionic baths, Phys. Rev. B 110, 115131 (2024).

Outline

Information

Phys. Rev. B 113, 235152– Published 25 June, 2026
  • Received 6 March 2026
  • Revised 18 May 2026
  • Accepted 1 June 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