- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

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

Enhancement of superconducting pairing via quantum Lyapunov control

Oleksandr Povitchan1,2,*, Denys I. Bondar3,†, and Andrii G. Sotnikov2,4,‡

  • 1Department of Physics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
  • 2Education and Research Institute “School of Physics and Technology”, Karazin Kharkiv National University, Svobody Square 4, 61022 Kharkiv, Ukraine
  • 3Department of Physics and Engineering Physics, Tulane University, 6823 St. Charles Avenue, New Orleans, Louisiana 70118, USA
  • 4Akhiezer Institute for Theoretical Physics, NSC KIPT, Akademichna 1, 61108 Kharkiv, Ukraine

  • *Contact author: opovitchan@student.ethz.ch
  • †Contact author: dbondar@tulane.edu
  • ‡Contact author: a_sotnikov@kipt.kharkov.ua
PDF

Phys. Rev. A 112, 033117 – Published 29 September, 2025

DOI: https://doi.org/10.1103/7dz3-2wlk

Abstract

We demonstrate that quantum Lyapunov control provides an effective strategy for enhancing superconducting correlations in the Fermi-Hubbard model without requiring careful parameter tuning. While photoinduced superconductivity is sensitive to the frequency and amplitude of a monochromatic laser pulse, our approach employs a simple feedback-based protocol that prevents the decrease of superconducting correlations once they begin to form. This method enables robust enhancement of pairing across a broad range of initial pumping conditions, eliminating the need for intricate frequency and amplitude optimization. We also show that an alternative implementation, asymptotic quantum control, achieves comparable results. Furthermore, our approach can be adapted to suppress previously induced superconducting correlations, providing bidirectional control over quantum pairing states. These findings suggest practical pathways for manipulating quantum correlations in strongly interacting systems with minimal experimental complexity.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (32)

  1. C. N. Yang, Concept of off-diagonal long-range order and the quantum phases of liquid He and of superconductors, Rev. Mod. Phys. 34, 694 (1962).
  2. C. N. Yang, η Pairing and off-diagonal long-range order in a Hubbard model, Phys. Rev. Lett. 63, 2144 (1989).
  3. H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka, and P. Werner, Nonequilibrium dynamical mean-field theory and its applications, Rev. Mod. Phys. 86, 779 (2014).
  4. M. A. Sentef, A. F. Kemper, A. Georges, and C. Kollath, Theory of light-enhanced phonon-mediated superconductivity, Phys. Rev. B 93, 144506 (2016).
  5. T. Kaneko, T. Shirakawa, S. Sorella, and S. Yunoki, Photoinduced η pairing in the Hubbard model, Phys. Rev. Lett. 122, 077002 (2019).
  6. T. Kaneko, S. Yunoki, and A. J. Millis, Charge stiffness and long-range correlation in the optically induced η-pairing state of the one-dimensional Hubbard model, Phys. Rev. Res. 2, 032027(R) (2020).
  7. D. Fausti, R. I. Tobey, N. Dean, S. Kaiser, A. Dienst, M. C. Hoffmann, S. Pyon, T. Takayama, H. Takagi, and A. Cavalleri, Light-induced superconductivity in a stripe-ordered cuprate, Science 331, 189 (2011).
  8. M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Riccò, S. R. Clark, D. Jaksch, and A. Cavalleri, Possible light-induced superconductivity in K3C60 at high temperature, Nature (London) 530, 461 (2016).
  9. A. Cantaluppi, M. Buzzi, G. Jotzu, D. Nicoletti, M. Mitrano, D. Pontiroli, M. Riccò, A. Perucchi, P. Di Pietro, and A. Cavalleri, Pressure tuning of light-induced superconductivity in K3C60, Nat. Phys. 14, 837 (2018).
  10. R. Kosloff, A. D. Hammerich, and D. Tannor, Excitation without demolition: Radiative excitation of ground-surface vibration by impulsive stimulated Raman scattering with damage control, Phys. Rev. Lett. 69, 2172 (1992).
  11. M. Sugawara and Y. Fujimura, Control of quantum dynamics by a locally optimized laser field. Application to ring puckering isomerization, J. Chem. Phys. 100, 5646 (1994).
  12. M. Sugawara and Y. Fujimura, Control of quantum dynamics by a locally optimized laser field. Multi-photon dissociation of hydrogen fluoride, Chem. Phys. 196, 113 (1995).
  13. Y. Ohtsuki, Y. Yahata, H. Kono, and Y. Fujimura, Application of a locally optimized control theory to pump–dump laser-driven chemical reactions, Chem. Phys. Lett. 287, 627 (1998).
  14. D. J. Tannor, R. Kosloff, and A. Bartana, Laser cooling of internal degrees of freedom of molecules by dynamically trapped states, Faraday Discuss. 113, 365 (1999).
  15. M. Sugawara, General formulation of locally designed coherent control theory for quantum system, J. Chem. Phys. 118, 6784 (2003).
  16. M. Mirrahimi, G. Turinici, and P. Rouchon, Reference trajectory tracking for locally designed coherent quantum controls, J. Phys. Chem. A 109, 2631 (2005).
  17. C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbrüggen, D. Sugny, and F. K. Wilhelm, Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe, EPJ Quantum Technol. 9, 19 (2022).
  18. O. V. Morzhin and A. N. Pechen, Krotov method for optimal control of closed quantum systems, Russ. Math. Surv. 74, 851 (2019).
  19. S. J. Glaser, U. Boscain, T. Calarco, C. P. Koch, W. Köckenberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, T. Schulte-Herbrüggen et al., Training Schrödinger's cat: Quantum optimal control, Eur. Phys. J. D 69, 279 (2015).
  20. I. Petersen and D. Dong, Quantum control theory and applications: A survey, IET Control Theory Appl. 4, 2651 (2010).
  21. C. Brif, R. Chakrabarti, and H. Rabitz, Control of quantum phenomena: Past, present and future, New J. Phys. 12, 075008 (2010).
  22. D. D'Alessandro, Introduction to Quantum Control and Dynamics (CRC Press, New York, 2021).
  23. A. B. Magann, K. M. Rudinger, M. D. Grace, and M. Sarovar, Lyapunov-control-inspired strategies for quantum combinatorial optimization, Phys. Rev. A 106, 062414 (2022).
  24. J. B. Larsen, M. D. Grace, A. D. Baczewski, and A. B. Magann, Feedback-based quantum algorithms for ground state preparation, Phys. Rev. Res. 6, 033336 (2024).
  25. I. Bloch, J. Dalibard, and S. Nascimbène, Quantum simulations with ultracold quantum gases, Nat. Phys. 8, 267 (2012).
  26. N. D. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17, 1133 (1966).
  27. A. Altland and B. D. Simons, Condensed Matter Field Theory, 2nd ed. (Cambridge University Press, Cambridge, 2010).
  28. P. Weinberg and M. Bukov, QuSpin: A Python package for dynamics and exact diagonalisation of quantum many body systems. Part I: Spin chains, SciPost Phys. 2, 003 (2017).
  29. P. Weinberg and M. Bukov, QuSpin: A Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: Bosons, fermions and higher spins, SciPost Phys. 7, 020 (2019).
  30. A. M. Lyapunov, The general problem of the stability of motion, Int. J. Control 55, 531 (1992).
  31. R. Rey-de Castro, R. Cabrera, D. I. Bondar, and H. Rabitz, Time-resolved quantum process tomography using Hamiltonian-encoding and observable-decoding, New J. Phys. 15, 025032 (2013).
  32. https://github.com/OleksandrPovitchan/SC-pairing-Q-control.

Outline

Information

Phys. Rev. A 112, 033117– Published 29 September, 2025
  • Received 28 March 2025
  • Revised 22 August 2025
  • Accepted 12 September 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