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  • Open Access

Josephson dynamics in two-dimensional ring-shaped condensates

Koon Siang Gan1,*,†, Vijay Pal Singh2,*, Luigi Amico2,3,4, and Rainer Dumke5,6

  • *These authors contributed equally to this work.
  • †Contact author: ksgan1@e.ntu.edu.sg
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Phys. Rev. Research 8, 023190 – Published 20 May, 2026

DOI: https://doi.org/10.1103/3249-x994

Abstract

We investigate Josephson transport in a fully closed, two-dimensional superfluid circuit formed by a ring-shaped Rb87 Bose-Einstein condensate that contains two optical barriers acting as movable weak links. Translating these barriers at controlled speeds imposes a steady bias current, enabling direct mapping of the current-chemical-potential (I−Δμ) characteristics. For narrow junctions (w≈1µm), the circuit exhibits a pronounced dc branch that terminates at a critical current Ic=9(1)×103s−1; above this threshold, the system switches to an ac, resistive regime. Classical-field simulations that include the moving barriers quantitatively reproduce both the nonlinear I−Δμ curve and the measured Ic, validating the underlying microscopic picture. Analysis of the ensuing phase dynamics shows that dissipation is mediated by the nucleation and traversal of vortex-antivortex pairs through the junctions, while the bulk condensate remains globally phase locked—direct evidence of the ring's topological constraint enforcing quantized circulation. These results establish a cold-atom analog of a superconducting quantum interference device in which Josephson dynamics can be resolved at the single-vortex level, providing a versatile platform for atomtronic circuit elements, nonreciprocal Josephson devices, and on-chip Sagnac interferometers for multiaxis rotation sensing.

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References (62)

  1. B. D. Josephson, Possible new effects in superconductive tunnelling, Phys. Lett. 1, 251 (1962).
  2. Advances in Superconductivity, edited by B. Deaver et al. (Plenum Press, New York, 1983).
  3. M. Tinkham, Introduction to Superconductivity (Dover Publications, Inc., Mineola, New York, 2004).
  4. A. Rashidi, S. Ahadi, and S. Stemmer, Self-field-induced Josephson diode effect, Nano Lett. 25, 10544 (2025).
  5. K. G. Fedorov, S. V. Shitov, H. Rotzinger, and A. V. Ustinov, Nonreciprocal microwave transmission through a long Josephson junction, Phys. Rev. B 85, 184512 (2012).
  6. L. Ozyuzer, A. E. Koshelev, C. Kurter, N. Gopalsami, Q. Li, M. Tachiki, K. Kadowaki, T. Yamamoto, H. Minami, H. Yamaguchi, et al., Emission of coherent THz radiation from superconductors, Science 318, 1291 (2007).
  7. A. J. Leggett, Macroscopic quantum tunnelling and related matters, Jpn. J. Appl. Phys. 26, 1986 (1987).
  8. A. J. Leggett, Macroscopic quantum systems and the quantum theory of measurement, Prog. Theor. Phys. Suppl. 69, 80 (1980).
  9. R. L. Fagaly, Superconducting quantum interference device instruments and applications, Rev. Sci. Inst. 77, 101101 (2006).
  10. L. Amico, D. Anderson, M. Boshier, J.-P. Brantut, L.-C. Kwek, A. Minguzzi, and W. von Klitzing, Colloquium: Atomtronic circuits: From many-body physics to quantum technologies, Rev. Mod. Phys. 94, 041001 (2022).
  11. J. Polo, W. J. Chetcuti, E. C. Domanti, P. Kitson, A. Osterloh, F. Perciavalle, V. P. Singh, and L. Amico, Perspective on new implementations of atomtronic circuits, Quantum Sci. Technol. 9, 030501 (2024).
  12. A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates, Phys. Rev. Lett. 79, 4950 (1997).
  13. W. J. Kwon, G. D. Pace, R. Panza, M. Inguscio, W. Zwerger, M. Zaccanti, F. Scazza, and G. Roati, Strongly correlated superfluid order parameters from dc Josephson supercurrents, Science 369, 84 (2020).
  14. N. Luick, L. Sobirey, M. Bohlen, V. P. Singh, L. Mathey, T. Lompe, and H. Moritz, An ideal Josephson junction in an ultracold two-dimensional Fermi gas, Science 369, 89 (2020).
  15. V. P. Singh, J. Polo, L. Mathey, and L. Amico, Shapiro steps in driven atomic Josephson junctions, Phys. Rev. Lett. 133, 093401 (2024).
  16. G. D. Pace, D. Hernández-Rajkov, V. P. Singh, N. Grani, M. F. Fernández, G. Nesti, J. A. Seman, M. Inguscio, L. Amico, and G. Roati, Shapiro steps in strongly-interacting Fermi gases, Science 390, 1125 (2025).
  17. E. Bernhart, M. Röhrle, V. P. Singh, L. Mathey, L. Amico, and H. Ott, Observation of Shapiro steps in an ultracold atomic Josephson junction, Science 390, 1130 (2025).
  18. V. P. Singh, L. Amico, and L. Mathey, Atomic Josephson parametric amplifier, Phys. Rev. Res. 8, L012067 (2026).
  19. M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Direct observation of tunneling and nonlinear self-trapping in a single Bosonic Josephson junction, Phys. Rev. Lett. 95, 010402 (2005).
  20. S. Levy, E. Lahoud, I. Shomroni, and J. Steinhauer, The a.c. and d.c. Josephson effects in a Bose–Einstein condensate, Nature (London) 449, 579 (2007).
  21. G. Del Pace, W. J. Kwon, M. Zaccanti, G. Roati, and F. Scazza, Tunneling transport of unitary Fermions across the superfluid transition, Phys. Rev. Lett. 126, 055301 (2021).
  22. V. P. Singh, E. Bernhart, M. Röhrle, H. Ott, L. Mathey, and L. Amico, Weak-link to tunneling regime in a 3D atomic Josephson junction, arXiv:2509.03591.
  23. S. Moulder, S. Beattie, R. P. Smith, N. Tammuz, and Z. Hadzibabic, Quantized supercurrent decay in an annular Bose-Einstein condensate, Phys. Rev. A 86, 013629 (2012).
  24. A. Ramanathan, K. C. Wright, S. R. Muniz, M. Zelan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tunable weak link, Phys. Rev. Lett. 106, 130401 (2011).
  25. G. Del Pace, K. Xhani, A. Muzi Falconi, M. Fedrizzi, N. Grani, D. Hernandez Rajkov, M. Inguscio, F. Scazza, W. J. Kwon, and G. Roati, Imprinting persistent currents in tunable Fermionic rings, Phys. Rev. X 12, 041037 (2022).
  26. Y. Cai, D. G. Allman, P. Sabharwal, and K. C. Wright, Persistent currents in rings of ultracold Fermionic atoms, Phys. Rev. Lett. 128, 150401 (2022).
  27. K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, Driving phase slips in a superfluid atom circuit with a rotating weak link, Phys. Rev. Lett. 110, 025302 (2013).
  28. F. Jendrzejewski, S. Eckel, N. Murray, C. Lanier, M. Edwards, C. J. Lobb, and G. K. Campbell, Resistive flow in a weakly interacting Bose-Einstein condensate, Phys. Rev. Lett. 113, 045305 (2014).
  29. F. Piazza, L. A. Collins, and A. Smerzi, Vortex-induced phase-slip dissipation in a toroidal Bose-Einstein condensate flowing through a barrier, Phys. Rev. A 80, 021601(R) (2009).
  30. S. Eckel, J. G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, Hysteresis in a quantized superfluid ‘atomtronic’ circuit, Nature (London) 506, 200 (2014).
  31. A. C. Mathey, C. W. Clark, and L. Mathey, Decay of a superfluid current of ultracold atoms in a toroidal trap, Phys. Rev. A 90, 023604 (2014).
  32. A. C. Mathey and L. Mathey, Realizing and optimizing an atomtronic SQUID, New J. Phys. 18, 055016 (2016).
  33. C. Ryu, P. W. Blackburn, A. A. Blinova, and M. G. Boshier, Experimental realization of Josephson junctions for an atom SQUID, Phys. Rev. Lett. 111, 205301 (2013).
  34. C. Ryu, E. C. Samson, and M. G. Boshier, Quantum interference of currents in an atomtronic SQUID, Nat. Commun. 11, 3338 (2020).
  35. H. Kiehn, V. P. Singh, and L. Mathey, Implementation of an atomtronic SQUID in a strongly confined toroidal condensate, Phys. Rev. Res. 4, 033024 (2022).
  36. J. Polo, W. Chetcuti, T. Haug, A. Minguzzi, K. Wright, and L. Amico, Persistent currents in ultracold gases, Phys. Rep. 1137, 1 (2025).
  37. K. Görg, L. Mathey, and V. P. Singh, Realizing an atomic quantum interference device in a rotating-box potential, Phys. Rev. Res. 7, 043340 (2025).
  38. G. Gauthier, I. Lenton, N. M. Parry, M. Baker, M. Davis, H. Rubinsztein-Dunlop, and T. Neely, Direct imaging of a digital-micromirror device for configurable microscopic optical potentials, Optica 3, 1136 (2016).
  39. G. Gauthier, T. A. Bell, A. B. Stilgoe, M. Baker, H. Rubinsztein-Dunlop, and T. W. Neely, Dynamic high-resolution optical trapping of ultracold atoms, Adv. Atomic Molecular Opt. Phys. 70, 1 (2021).
  40. M. Aidelsburger, J. L. Ville, R. Saint-Jalm, S. Nascimbène, J. Dalibard, and J. Beugnon, Relaxation dynamics in the merging of n independent condensates, Phys. Rev. Lett. 119, 190403 (2017).
  41. L. Pezzè, K. Xhani, C. Daix, N. Grani, B. Donelli, F. Scazza, D. Hernandez-Rajkov, W. J. Kwon, G. Del Pace, and G. Roati, Stabilizing persistent currents in an atomtronic Josephson junction necklace, Nat. Commun. 15, 4831 (2024).
  42. S. Sunami, V. P. Singh, D. Garrick, A. Beregi, A. J. Barker, K. Luksch, E. Bentine, L. Mathey, and C. J. Foot, Observation of the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional Bose gas via matter-wave interferometry, Phys. Rev. Lett. 128, 250402 (2022).
  43. O. Morizot, Y. Colombe, V. Lorent, H. Perrin, and B. M. Garraway, Ring trap for ultracold atoms, Phys. Rev. A 74, 023617 (2006).
  44. Z. Hadzibabic and J. Dalibard, Two-dimensional Bose fluids: An atomic physics perspective, Riv. Nuovo Cimento 34, 389 (2011).
  45. P. B. Blakie, A. Bradley, M. Davis, R. Ballagh, and C. Gardiner, Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques, Adv. Phys. 57, 363 (2008).
  46. A. Polkovnikov, Phase space representation of quantum dynamics, Ann. Phys. 325, 1790 (2010).
  47. V. P. Singh, C. Weitenberg, J. Dalibard, and L. Mathey, Superfluidity and relaxation dynamics of a laser-stirred two-dimensional Bose gas, Phys. Rev. A 95, 043631 (2017).
  48. V. P. Singh and L. Mathey, Collective modes and superfluidity of a two-dimensional ultracold Bose gas, Phys. Rev. Res. 3, 023112 (2021).
  49. V. P. Singh, N. Luick, L. Sobirey, and L. Mathey, Josephson junction dynamics in a two-dimensional ultracold Bose gas, Phys. Rev. Res. 2, 033298 (2020).
  50. C. Ryu, M. F. Andersen, P. Cladé, V. Natarajan, K. Helmerson, and W. D. Phillips, Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap, Phys. Rev. Lett. 99, 260401 (2007).
  51. A. V. Ustinov, Solitons in Josephson junctions, Physica D 123, 315 (1998).
  52. B. Pal, A. Chakraborty, P. K. Sivakumar, M. Davydova, A. K. Gopi, A. K. Pandeya, J. A. Krieger, Y. Zhang, M. Date, S. Ju, N. Yuan, N. B. M. Schröter, L. Fu, and S. S. P. Parkin, Josephson diode effect from Cooper pair momentum in a topological semimetal, Nat. Phys. 18, 1228 (2022).
  53. H. Wu, Y. Wang, Y. Xu, P. K. Sivakumar, C. Pasco, U. Filippozzi, S. S. P. Parkin, Y.-J. Zeng, T. McQueen, and M. N. Ali, The field-free Josephson diode in a van der Waals heterostructure, Nature (London) 604, 653 (2022).
  54. W. Gou, T. Chen, D. Xie, T. Xiao, T.-S. Deng, B. Gadway, W. Yi, and B. Yan, Tunable nonreciprocal quantum transport through a dissipative Aharonov–Bohm ring, Phys. Rev. Lett. 124, 070402 (2020).
  55. J. W. Z. Lau, K. S. Gan, R. Dumke, L. Amico, L.-C. Kwek, and T. Haug, Atomtronic multiterminal Aharonov-Bohm interferometer, Phys. Rev. A 107, L051303 (2023).
  56. T. L. Gustavson, P. Bouyer, and M. A. Kasevich, Precision rotation measurements with an atom interferometer gyroscope, Phys. Rev. Lett. 78, 2046 (1997).
  57. S. M. Dickerson, J. M. Hogan, A. Sugarbaker, David M. S. Johnson, and M. A. Kasevich, Multiaxis inertial sensing with long-time point source atom interferometry, Phys. Rev. Lett. 111, 083001 (2013).
  58. B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Bordé, A. Landragin, and P. Bouyer, Six-axis inertial sensor using cold-atom interferometry, Phys. Rev. Lett. 97, 010402 (2006).
  59. K. A. Krzyzanowska, J. Ferreras, C. Ryu, E. C. Samson, and M. G. Boshier, Matter-wave analog of a fiber-optic gyroscope, Phys. Rev. A 108, 043305 (2023).
  60. E. Strambini, A. Iorio, O. Durante, R. Citro, C. Sanz-Fernández, C. Guarcello, I. V. Tokatly, A. Braggio, and F. Giazotto, A Josephson phase battery, Nat. Nanotechnol. 15, 656 (2020).
  61. J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, Josephson persistent-current qubit, Science 285, 1036 (1999).
  62. L. B. Ioffe, M. V. Feigel'man, A. Ioselevich, D. Ivanov, M. Troyer, and G. Blatter, Topologically protected quantum bits using Josephson junction arrays, Nature (London) 415, 503 (2002).

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Phys. Rev. Research 8, 023190– Published 20 May, 2026
  • Received 11 September 2025
  • Accepted 13 April 2026
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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.

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