- 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

Quantum dynamics in multiple baths: Initial baths separability condition for noninterference

Li Yu1 and Eric J. Heller1,2

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA

PDF

Phys. Rev. Research 7, 033113 – Published 1 August, 2025

DOI: https://doi.org/10.1103/rd78-ywr8

Abstract

We use a master equation to provide a proof of interference between noninteracting baths on a system’s reduced dynamics, agreeing with a result in Phys. Rev. A 89, 042117 (2014). Here, we provide a formula for the details of leading-order interference. We illustrate the use of such interference toward suppressing (even freezing) decoherence with a simplest example and identify what determines the extent of decoherence suppression. However, we find that interference of baths vanishes (up to second order) as long as the baths are initially separable, thereby identifying a “low-bar” condition for noninterference. This finding provides strong justification for the widely used “additive assumption” in weak coupling regime. We discuss how this noninterference finding sheds light on the “puzzle” of vanishing second-order interference in the joint scenario of quantum and classical noises in arXiv:2004.13901. We also provide a general proof of interference between two baths under stochastic coupling, in contrast to the study of deterministic coupling in the literature. We demonstrate decoherence suppression with an example of a central spin stochastically coupled to two environmental spins. We find that two baths will cease to interfere (up to second order) if the two baths are initially separable and the system’s stochastic coupling strengths with the two baths are uncorrelated.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (37)

  1. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, New York, 2002).
  2. M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition (Springer, New York, 2007).
  3. C.-K. Chan, G.-D. Lin, S. F. Yelin, and M. D. Lukin, Quantum interference between independent reservoirs in open quantum systems, Phys. Rev. A 89, 042117 (2014).
  4. L. Lamata, D. R. Leibrandt, I. L. Chuang, J. I. Cirac, M. D. Lukin, V. Vuletic, and S. F. Yelin, Ion crystal transducer for strong coupling between single ions and single photons, Phys. Rev. Lett. 107, 030501 (2011).
  5. J. Gea-Banacloche, T. C. Burt, P. R. Rice, and L. A. Orozco, Entangled and disentangled evolution for a single atom in a driven cavity, Phys. Rev. Lett. 94, 053603 (2005).
  6. G.-D. Lin and L.-M. Duan, Equilibration and temperature distribution in a driven ion chain, New J. Phys. 13, 075015 (2011).
  7. E. Ferraro, M. Scala, R. Migliore, and A. Napoli, Non-Markovian dissipative dynamics of two coupled qubits in independent reservoirs: Comparison between exact solutions and master-equation approaches, Phys. Rev. A 80, 042112 (2009).
  8. B. Bellomo, R. Lo Franco, S. Maniscalco, and G. Compagno, Entanglement trapping in structured environments, Phys. Rev. A 78, 060302 (2008).
  9. D. Gribben, D. M. Rouse, J. Iles-Smith, A. Strathearn, H. Maguire, P. Kirton, A. Nazir, E. M. Gauger, and B. W. Lovett, Exact dynamics of nonadditive environments in non-Markovian open quantum systems, PRX Quantum 3, 010321 (2022).
  10. S. Luo, N. Lambert, P. Liang, and M. Cirio, Quantum-classical decomposition of Gaussian quantum environments: A stochastic pseudomode model, PRX Quantum 4, 030316 (2023).
  11. J. Garwoła and D. Segal, Open quantum systems with noncommuting coupling operators: An analytic approach, Phys. Rev. B 110, 174304 (2024).
  12. C. R. Hogg, F. Cerisola, J. D. Cresser, S. A. R. Horsley, and J. Anders, Enhanced entanglement in multi-bath spin-boson models, Quantum 8, 1357 (2024).
  13. S. Koyanagi and Y. Tanimura, Hierarchical equations of motion for multiple baths (HEOM-MB) and their application to Carnot cycle, J. Chem. Phys. 161, 162501 (2024).
  14. H.-Y. Qi, Y. Su, Y. Wang, R.-X. Xu, and Y.-J. Yan, Extended system-bath entanglement theorem with multiple baths in the presence of external fields, J. Chem. Phys. 161, 124104 (2024).
  15. G. G. Giusteri, F. Recrosi, G. Schaller, and G. L. Celardo, Interplay of different environments in open quantum systems: Breakdown of the additive approximation, Phys. Rev. E 96, 012113 (2017).
  16. J. Kołodyński, J. B. Brask, M. Perarnau-Llobet, and B. Bylicka, Adding dynamical generators in quantum master equations, Phys. Rev. A 97, 062124 (2018).
  17. M. T. Mitchison and M. B. Plenio, Non-additive dissipation in open quantum networks out of equilibrium, New J. Phys. 20, 033005 (2018).
  18. H. Maguire, J. Iles-Smith, and A. Nazir, Environmental non-additivity and Franck-Condon physics in non-equilibrium quantum systems, Phys. Rev. Lett. 123, 093601 (2019).
  19. C. McConnell and A. Nazir, Electron counting statistics for non-additive environments, J. Chem. Phys. 151, 054104 (2019).
  20. J. Jing, T. Yu, C.-H. Lam, J. Q. You, and L.-A. Wu, Control relaxation via dephasing: A quantum-state-diffusion study, Phys. Rev. A 97, 012104 (2018).
  21. Note that the term “bath” is sometimes used to only refer to a thermal bath in the literature, that is, an environment (or reservoir) in a thermal equilibrium state. Here, we are loosely using “bath” to mean any environment, be it thermal or not.
  22. L. Yu and E. J. Heller, A formally exact master equation for open quantum systems, arXiv:2004.13130.
  23. L. Yu and E. J. Heller, Corrections to effective coupling: A master equation for stochastic system-bath coupling, manuscript in preparation.
  24. M. Leijnse and M. R. Wegewijs, Kinetic equations for transport through single-molecule transistors, Phys. Rev. B 78, 235424 (2008).
  25. S. Koller, M. Grifoni, M. Leijnse, and M. R. Wegewijs, Density-operator approaches to transport through interacting quantum dots: Simplifications in fourth-order perturbation theory, Phys. Rev. B 82, 235307 (2010).
  26. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, New York, 2010), 2nd ed.
  27. M. Shapiro and P. Brumer, Quantum Control of Molecular Processes (Wiley-VCH, Weinheim, Germany, 2012), 2nd revised and enlarged edition.
  28. L. Viola and S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A 58, 2733 (1998).
  29. D. Vitali and P. Tombesi, Using parity kicks for decoherence control, Phys. Rev. A 59, 4178 (1999).
  30. L. Hao, W. Huo, and G. Long, Dynamical decoupling method for the suppression of decoherence of the delta-type three-level atom with finite control pulse length, J. Phys. B: At. Mol. Opt. Phys. 41, 125501 (2008).
  31. J. Lee, Y. Jeong, Y. Kim, and Y. Kim, Experimental demonstration of decoherence suppression via quantum measurement reversal, Opt. Express 19, 16309 (2011).
  32. J. Lee, H. Lim, K. Hong, Y. Jeong, M. S. Kim, and Y. Kim, Experimental demonstration of delayed-choice decoherence suppression, Nat. Commun. 5, 4522 (2014).
  33. S. Xue, R. Wu, W. Zhang, J. Zhang, C. Li, and T. Tarn, Decoherence suppression via non-Markovian coherent feedback control, Phys. Rev. A 86, 052304 (2012).
  34. R. Shankar, Principles of Quantum Mechanics (Plenum Press, New York, 1994), 2nd ed.
  35. More precisely, we mean that the baths are statistically independent at initial time. Thus, there is neither quantum correlation nor classical correlation between them. Note that the term “separability” sometimes refers to the absence of quantum correlation without regard to classical correlation, for example, in the quantum information literature, but that is not the same as what we mean here.
  36. To be precise, what we mean is, without the condition of initially separable baths as in Eq. (38), we are not guaranteed the validity of the additive assumption and may not assume it a priori. Therefore, initial nonseparability of baths may, but does not necessarily, lead to the failure of the additive assumption.
  37. L. Yu, Unifying the dynamical effects of quantum and classical noises, arXiv:2004.13901.

Outline

Information

Phys. Rev. Research 7, 033113– Published 1 August, 2025
  • Received 17 April 2025
  • Accepted 15 July 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