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Control of memory effects in a spin-boson system by periodic driving

Pietro Marco Follia1,2,*, Bassano Vacchini1,2, and Heinz-Peter Breuer3,4

  • *Contact author: pietro.follia@unimi.it
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Phys. Rev. A 113, 022203 – Published 3 February, 2026

DOI: https://doi.org/10.1103/g55y-8j7x

Abstract

We study the emergence of quantum memory effects in a spin-boson system at finite temperature driven by an external time-periodic force. Quantifying memory effects by the trace-distance based measure for non-Markovianity and performing numerical simulations employing the hierarchical equations of motion approach, we find a pronounced peak structure when plotting the non-Markovianity measure as a function of the driving amplitude. This distinctive feature is interpreted using Floquet theory and the Floquet-Lindblad master equation, associating the peaks with the degeneracies of the quasienergy spectrum which lead to a strong enhancement of the relaxation times of the system. These results suggest strategies for the efficient control of non-Markovianity in open quantum systems by periodic driving.

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References (44)

  1. H.-P. Breuer and F. Petruccione, The Theory of Open Quanutm Systems, 1st ed. (Oxford University Press, Oxford, 2002).
  2. B. Vacchini, Open Quantum Systems: Foundations and Theory, Graduate Texts in Physics (Springer Nature, Cham, 2024).
  3. Á. Rivas, S. F. Huelga, and M. B. Plenio, Quantum non-Markovianity: Characterization, quantification and detection, Rep. Prog. Phys. 77, 094001 (2014).
  4. H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini, Colloquium: Non-Markovian dynamics in open quantum systems, Rev. Mod. Phys. 88, 021002 (2016).
  5. L. Li, M. J. Hall, and H. M. Wiseman, Concepts of quantum non-Markovianity: A hierarchy, Phys. Rep. 759, 1 (2018).
  6. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Dynamics of the dissipative two-state system, Rev. Mod. Phys. 59, 1 (1987).
  7. R. Marcus and N. Sutin, Electron transfers in chemistry and biology, Biochim. Biophys. Acta Bioenerg. 811, 265 (1985).
  8. H. G. U. Weiss and S. Linkwitz, Influence of friction and temperature on coherent quantum tunneling, J. Low. Temp. Phys. 68, 213 (1987).
  9. Z. Huang, P. S. Mundada, A. Gyenis, D. I. Schuster, A. A. Houck, and J. Koch, Engineering dynamical sweet spots to protect qubits from 1/f noise, Phys. Rev. Appl. 15, 034065 (2021).
  10. P. S. Mundada, A. Gyenis, Z. Huang, J. Koch, and A. A. Houck, Floquet-engineered enhancement of coherence times in a driven fluxonium qubit, Phys. Rev. Appl. 14, 054033 (2020).
  11. G. Clos and H.-P. Breuer, Quantification of memory effects in the spin-boson model, Phys. Rev. A 86, 012115 (2012).
  12. S. Wenderoth, H.-P. Breuer, and M. Thoss, Non-Markovian effects in the spin-boson model at zero temperature, Phys. Rev. A 104, 012213 (2021).
  13. G. Amati, Dynamical signatures of non-Markovianity in a dissipative-driven qubit, Phys. Rev. A 109, 052433 (2024).
  14. H.-P. Breuer, E.-M. Laine, and J. Piilo, Measure for the degree of non-Markovian behavior of quantum processes in open systems, Phys. Rev. Lett. 103, 210401 (2009).
  15. Y. Tanimura, Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (HEOM), J. Chem. Phys. 153, 020901 (2020).
  16. R. Blümel, A. Buchleitner, R. Graham, L. Sirko, U. Smilansky, and H. Walther, Dynamical localization in the microwave interaction of Rydberg atoms: The influence of noise, Phys. Rev. A 44, 4521 (1991).
  17. H.-P. Breuer and F. Petruccione, Dissipative quantum systems in strong laser fields: Stochastic wave-function method and Floquet theory, Phys. Rev. A 55, 3101 (1997).
  18. B. Vacchini, A. Smirne, E.-M. Laine, J. Piilo, and H.-P. Breuer, Markovianity and non-Markovianity in quantum and classical systems, New J. Phys. 13, 093004 (2011).
  19. S. Wißmann, H.-P. Breuer, and B. Vacchini, Generalized trace-distance measure connecting quantum and classical non-Markovianity, Phys. Rev. A 92, 042108 (2015).
  20. D. Chruściński, Dynamical maps beyond Markovian regime, Phys. Rep. 992, 1 (2022).
  21. A. Rivas, S. F. Huelga, and M. B. Plenio, Entanglement and non-Markovianity of quantum evolutions, Phys. Rev. Lett. 105, 050403 (2010).
  22. S. Luo, S. Fu, and H. Song, Quantifying non-Markovianity via correlations, Phys. Rev. A 86, 044101 (2012).
  23. M. Hayashi, Quantum Information (Springer-Verlag, Berlin, 2010).
  24. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University, New York, 2010).
  25. N. Megier, A. Smirne, and B. Vacchini, Entropic bounds on information backflow, Phys. Rev. Lett. 127, 030401 (2021).
  26. U. Weiss, Quantum Dissipative Systems, 4th ed. (World Scientific, Singapore, 2012).
  27. 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).
  28. Y.-T. Huang, P.-C. Kuo, N. Lambert, M. Cirio, S. Cross, S.-L. Yang, F. Nori, and Y.-N. Chen, An efficient Julia framework for hierarchical equations of motion in open quantum systems, Commun. Phys. 6, 313 (2023).
  29. R. P. Feynman and F. L. Vernon, The theory of a general quantum system intearacting with a linear dissipative system, Ann. Phys. (NY) 24, 118 (1963).
  30. J. Hu, M. Luo, F. Jiang, R.-X. Xu, and Y. Yan, Padé spectrum decompositions of quantum distribution functions and optimal hierarchical equations of motion construction for quantum open systems, J. Chem. Phys. 134, 244106 (2011).
  31. H. P. Breuer, K. Dietz, and M. Holthaus, The role of avoided crossings in the dynamics of strong laser field–matter interactions, Z. Phys. D 8, 349 (1988).
  32. H. P. Breuer, K. Dietz, and M. Holthaus, Strong laser fields interacting with matter I, Z. Phys. D 10, 13 (1988).
  33. Y. B. Zeldovich, The quasienergy of a quantum-mechanical system subjected to a periodic action, J. Exptl. Theoret. Phys. (U.S.S.R.) 51, 1492 (1966) [Sov. Phys. JETP 24, 1006 (1967)].
  34. J. H. Shirley, Solution of the Schrödinger equation with a Hamiltonian periodic in time, Phys. Rev. 138, B979 (1965).
  35. V. I. Ritus, Shift and splitting of atomic energy levels by the field of an electromagnetic wave, J. Exptl. Theoret. Phys. (U.S.S.R.) 51, 1544 (1966) [Sov. Phys. JETP 24, 1041 (1967)].
  36. H. Sambe, Steady states and quasienergies of a quantum-mechanical system in an oscillating field, Phys. Rev. A 7, 2203 (1973).
  37. N. Goldman and J. Dalibard, Periodically driven quantum systems: Effective Hamiltonians and engineered gauge fields, Phys. Rev. X 4, 031027 (2014).
  38. M. Holthaus, Floquet engineering with quasienergy bands of periodically driven optical lattices, J. Phys. B 49, 013001 (2016).
  39. T. Ikeda, K. Chinzei, and M. Sato, Nonequilibrium steady states in the Floquet-Lindblad systems: van Vleck's high-frequency expansion approach, SciPost Phys. Core 4, 033 (2021).
  40. T. Mori, Floquet states in open quantum systems, Annu. Rev. Condens. Matter Phys. 14, 35 (2023).
  41. K. M. Fonseca-Romero, S. Kohler, and P. Hänggi, Coherence control for qubits, Chem. Phys. 296, 307 (2004).
  42. O. Benhayoune-Khadraoui, C. Lledó, and A. Blais, How the Kerr-Cat qubit dies-and how to rescue it, arXiv:2507.06160.
  43. S. Wißmann, A. Karlsson, E.-M. Laine, J. Piilo, and H.-P. Breuer, Optimal state pairs for non-Markovian quantum dynamics, Phys. Rev. A 86, 062108 (2012).
  44. P. M. Follia, B. Vacchini, and H.-P. Breuer, Replication data for: “Control of memory effects in a spin-boson system by periodic driving,” UNIMI Dataverse (2026), https://doi.org/doi:10.13130/RD_UNIMI/JZKPOY.

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Phys. Rev. A 113, 022203– Published 3 February, 2026
  • Received 1 August 2025
  • Revised 30 October 2025
  • Accepted 13 January 2026
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