- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Letters

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Quantum Theory of the Josephson Junction between Finite Islands

Thomas J. Maldonado*, Alejandro W. Rodriguez, and Hakan E. Türeci

  • Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA

  • *Contact author: maldonado@princeton.edu
PDF

Phys. Rev. Lett. 135, 120202 – Published 18 September, 2025

DOI: https://doi.org/10.1103/mwvt-wlkj

Abstract

Superconducting circuits comprising Josephson junctions have spurred significant research activity due to their promise to realize scalable quantum computers. Effective Hamiltonians for these systems have traditionally been derived assuming the junction connects superconducting islands of infinite size. We derive a quantized Hamiltonian for a Josephson junction between finite-sized islands and predict measurable corrections to the qubit frequency and charge susceptibility to test the theory.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (31)

  1. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  2. A. Griffin, D. W. Snoke, and S. Stringari, Bose-Einstein Condensation (Cambridge University Press, 1996).
  3. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Observation of Bose-Einstein condensation in a dilute atomic vapor, Science 269, 198 (1995).
  4. K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Bose-Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett. 75, 3969 (1995).
  5. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
  6. V. L. Ginzburg and L. D. Landau, On the Theory of Superconductivity, in On Superconductivity and Superfluidity (Springer, Berlin, Heidelberg, 2009), pp 113–137.
  7. W. Bao, D. Jaksch, and P. A. Markowich, Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation, J. Comput. Phys. 187, 318 (2003).
  8. B. D. Josephson, Possible new effects in superconductive tunnelling, Phys. Lett. 1, 251 (1962).
  9. B. Josephson, Supercurrents through barriers, Adv. Phys. 14, 419 (1965).
  10. R. Gati and M. K. Oberthaler, A bosonic Josephson junction, J. Phys. B 40, R61 (2007).
  11. T. J. Maldonado, H. E. Türeci, and A. W. Rodriguez, Mesoscopic theory of the Josephson junction, Phys. Rev. B 111, L140505 (2025).
  12. S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping, Phys. Rev. A 59, 620 (1999).
  13. J. Links, A. Foerster, A. P. Tonel, and G. Santos, The two-site Bose–Hubbard model, Ann. Henri Poincaré 7, 1591 (2006).
  14. G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential, Phys. Rev. A 55, 4318 (1997).
  15. A. J. Leggett, Bose-Einstein condensation in the alkali gases: Some fundamental concepts, Rev. Mod. Phys. 73, 307 (2001).
  16. F. Benatti, R. Floreanini, and J. Realpe-Gomez, Cooper pair boxes weakly coupled to external environments, J. Phys. A 41, 235304 (2008).
  17. R. Alicki, F. Benatti, and R. Floreanini, Charge oscillations in superconducting nanodevices coupled to external environments, Phys. Lett. A 372, 1968 (2008).
  18. L. Dell’Anna, Analytical approach to the two-site Bose-Hubbard model: From Fock states to Schrödinger cat states and entanglement entropy, Phys. Rev. A 85, 053608 (2012).
  19. J. Schwinger, On Angular Momentum, Tech. Rep., Harvard University; Nuclear Development Associates, Inc. (US), 1952, 10.2172/4389568.
  20. J. Von Delft and D. C. Ralph, Spectroscopy of discrete energy levels in ultrasmall metallic grains, Phys. Rep. 345, 61 (2001).
  21. K. Bladh, T. Duty, D. Gunnarsson, and P. Delsing, The single Cooper-pair box as a charge qubit, New J. Phys. 7, 180 (2005).
  22. A. Cottet, Implementation of a quantum bit in a superconducting circuit, Ph.D. thesis, Université Paris, 2002.
  23. J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76, 042319 (2007).
  24. M. Kristen, A. Schneider, A. Stehli, T. Wolz, S. Danilin, H. S. Ku, J. Long, X. Wu, R. Lake, D. P. Pappas et al., Amplitude and frequency sensing of microwave fields with a superconducting transmon qudit, npj Quantum Inf. 6, 57 (2020).
  25. A. Kringhøj, B. Van Heck, T. W. Larsen, O. Erlandsson, D. Sabonis, P. Krogstrup, L. Casparis, K. D. Petersson, and C. M. Marcus, Suppressed charge dispersion via resonant tunneling in a single-channel transmon, Phys. Rev. Lett. 124, 246803 (2020).
  26. C. Kittel and P. McEuen, Introduction to Solid State Physics (John Wiley & Sons, New York, 2018).
  27. V. Bouchiat, D. Vion, P. Joyez, D. Esteve, and M. Devoret, Quantum coherence with a single Cooper pair, Phys. Scr. 1998, 165 (1998).
  28. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940).
  29. J. G. Hirsch, O. Castanos, R. López-Pena, and E. Nahmad-Achar, Virtues and limitations of the truncated Holstein–Primakoff description of quantum rotors, Phys. Scr. 87, 038106 (2013).
  30. G. Catelani, Parity switching and decoherence by quasiparticles in single-junction transmons, Phys. Rev. B 89, 094522 (2014).
  31. T. J. Maldonado, finite-island-josephson (2025), GitHub repository archived on Zenodo, https://zenodo.org/records/16835078.

Outline

Information

Phys. Rev. Lett. 135, 120202– Published 18 September, 2025
  • Received 16 May 2025
  • Accepted 8 August 2025
Crossmark - Check for updates button

© 2025 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation