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Nonclassical photon-assisted transport in superconducting tunnel junctions

Matthias Hübler1, Juan Carlos Cuevas2,3, and Wolfgang Belzig1

Phys. Rev. B 112, 214501 – Published 1 December, 2025

DOI: https://doi.org/10.1103/64gy-9vnc

Abstract

Advances in circuit quantum electrodynamics have enabled the generation of arbitrary nonclassical microwave states, enabling progress in physics. Here, we present a theoretical study of the electrical current in a Josephson tunnel junction interacting with a nonclassical electromagnetic environment. This allows us to generalize classical transport phenomena like photon-assisted tunneling and Shapiro steps to the quantum regime. We predict that the analysis of the supercurrent in such a setup enables the complete reconstruction of quantum states of the electromagnetic environment, something that is not possible with normal tunnel junctions.

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References (32)

  1. A. Barone and G. Paterno, Physics and Applications of the Josephson Effect (John Wiley & Sons, New York, 1982).
  2. A. H. Dayem and R. J. Martin, Quantum interaction of microwave radiation with tunneling between superconductors, Phys. Rev. Lett. 8, 246 (1962).
  3. P. K. Tien and J. P. Gordon, Multiphoton process observed in the interaction of microwave fields with the tunneling between superconductor films, Phys. Rev. 129, 647 (1963).
  4. S. Shapiro, Josephson currents in superconducting tunneling: The effect of microwaves and other observations, Phys. Rev. Lett. 11, 80 (1963).
  5. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  6. A. A. Clerk, K. W. Lehnert, P. Bertet, J. R. Petta, and Y. Nakamura, Hybrid quantum systems with circuit quantum electrodynamics, Nat. Phys. 16, 257 (2020).
  7. M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O'connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, Synthesizing arbitrary quantum states in a superconducting resonator, Nature (London) 459, 546 (2009).
  8. L. Bretheau, Ç. Ö. Girit, H. Pothier, D. Esteve, and C. Urbina, Exciting Andreev pairs in a superconducting atomic contact, Nature (London) 499, 312 (2013).
  9. L. Bretheau, Ç. Girit, M. Houzet, H. Pothier, D. Esteve, and C. Urbina, Theory of microwave spectroscopy of Andreev bound states with a Josephson junction, Phys. Rev. B 90, 134506 (2014).
  10. G. Aiello, M. Féchant, A. Morvan, J. Basset, M. Aprili, J. Gabelli, and J. Estève, Quantum bath engineering of a high impedance microwave mode through quasiparticle tunneling, Nat. Commun. 13, 7146 (2022).
  11. J.-R. Souquet, M. J. Woolley, J. Gabelli, P. Simon, and A. A. Clerk, Photon-assisted tunneling with nonclassical light, Nat. Commun. 5, 5562 (2014).
  12. Y. V. Nazarov, Quantum Noise in Mesoscopic Physics, NATO Science Series II: Mathematics, Physics and Chemistry (Springer Science & Business Media, Dordrecht, 2012), Vol. 97.
  13. M. Vanević, Y. V. Nazarov, and W. Belzig, Elementary events of electron transfer in a voltage-driven quantum point contact, Phys. Rev. Lett. 99, 076601 (2007).
  14. M. Vanević, Y. V. Nazarov, and W. Belzig, Elementary charge-transfer processes in mesoscopic conductors, Phys. Rev. B 78, 245308 (2008).
  15. M. Kindermann and Y. V. Nazarov, Interaction effects on counting statistics and the transmission distribution, Phys. Rev. Lett. 91, 136802 (2003).
  16. M. Kindermann, Y. V. Nazarov, and C. W. J. Beenakker, Feedback of the electromagnetic environment on current and voltage fluctuations out of equilibrium, Phys. Rev. B 69, 035336 (2004).
  17. J. Tobiska and Y. V. Nazarov, Inelastic interaction corrections and universal relations for full counting statistics in a quantum contact, Phys. Rev. B 72, 235328 (2005).
  18. G.-L. Ingold and Y. V. Nazarov, Charge tunneling rates in ultrasmall junctions, in Single Charge Tunneling: Coulomb Blockade Phenomena In Nanostructures, edited by H. Grabert and M. H. Devoret (Springer US, Boston, MA, 1992), pp. 21–107.
  19. P. Joyez, Self-consistent dynamics of a Josephson junction in the presence of an arbitrary environment, Phys. Rev. Lett. 110, 217003 (2013).
  20. H. Grabert, Dynamical Coulomb blockade of tunnel junctions driven by alternating voltages, Phys. Rev. B 92, 245433 (2015).
  21. L. S. Levitov, H. Lee, and G. B. Lesovik, Electron counting statistics and coherent states of electric current, J. Math. Phys. 37, 4845 (1996).
  22. W. Belzig, Full counting statistics of superconductor-normal-metal heterostructures, in Quantum Noise in Mesoscopic Physics, edited by Y. V. Nazarov (Springer, Netherlands, Dordrecht, 2003), pp. 463–496.
  23. I. Snyman and Y. V. Nazarov, Keldysh action of a multiterminal time-dependent scatterer, Phys. Rev. B 77, 165118 (2008).
  24. Y. V. Nazarov, Full counting statistics and field theory, Ann. Phys. 519, 720 (2007).
  25. Y. M. Blanter and M. Büttiker, Shot noise in mesoscopic conductors, Phys. Rep. 336, 1 (2000).
  26. Y. V. Nazarov, Block-determinant formalism for an action of a multi-terminal scatterer, Physica E 74, 561 (2015).
  27. W. Belzig and Y. V. Nazarov, Full counting statistics of electron transfer between superconductors, Phys. Rev. Lett. 87, 197006 (2001).
  28. J. C. Cuevas and W. Belzig, Full counting statistics of multiple Andreev reflections, Phys. Rev. Lett. 91, 187001 (2003).
  29. J. C. Cuevas and W. Belzig, Dc transport in superconducting point contacts: A full-counting-statistics view, Phys. Rev. B 70, 214512 (2004).
  30. M. Hübler and W. Belzig, Full counting statistics of ultrafast quantum transport, Appl. Phys. Lett. 123, 034006 (2023).
  31. B. D. Josephson, Possible new effects in superconductive tunnelling, Phys. Lett. 1, 251 (1962).
  32. C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University Press, Cambridge, 2023).

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