- 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
  • Letter
  • Open Access

Atomic Josephson parametric amplifier

Vijay Pal Singh1,*, Luigi Amico1,2,3, and Ludwig Mathey4,5

  • *Contact author: vijay.singh@tii.ae
PDF

Phys. Rev. Research 8, L012067 – Published 20 March, 2026

DOI: https://doi.org/10.1103/7s1n-ddp9

Abstract

We study the dynamics of a driven atomic Josephson junction that we propose as a parametric amplifier. By periodically modulating the position of the barrier, we induce a small current across the junction, serving as our input signal. The pump field is implemented by modulating the barrier height at twice the Josephson plasma frequency. The resulting dynamics exhibit parametric amplification of the signal through nonlinear mixing between the signal and pump fields, which is encoded in a specific microscopic pattern of density waves and phase excitations that can be addressed within the experimental cold-atom capabilities. This work paves the way for tunable amplifiers in atomtronic circuits, with potential applications in several fields including precision measurements and quantum information processing. At the same time, our analysis provides the microscopic explanation of the general notion of parametric amplification occurring in nonlinear coherent devices.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (72)

  1. W. B. Case, The pumping of a swing from the standing position, Am. J. Phys. 64, 215 (1996).
  2. T.G. van de Roer, Microwave Electronic Devices, Microwave Technology Series (Chapman & Hall, United Kingdom, 1994).
  3. B. R. Mollow and R. J. Glauber, Quantum theory of parametric amplification. I, Phys. Rev. 160, 1076 (1967).
  4. R. Baumgartner and R. Byer, Optical parametric amplification, IEEE J. Quantum Electron. 15, 432 (1979).
  5. I. Thomson and G. Janssens, High reliability parametric amplifier varactor diodes for satellite applications, Microelectron. Reliab. 15, 563 (1976).
  6. B. Yurke, Squeezed-state generation using a Josephson parametric amplifier, J. Opt. Soc. Am. B 4, 1551 (1987).
  7. B. Yurke, L. R. Corruccini, P. G. Kaminsky, L. W. Rupp, A. D. Smith, A. H. Silver, R. W. Simon, and E. A. Whittaker, Observation of parametric amplification and deamplification in a Josephson parametric amplifier, Phys. Rev. A 39, 2519 (1989).
  8. I. Siddiqi, R. Vijay, F. Pierre, C. M. Wilson, M. Metcalfe, C. Rigetti, L. Frunzio, and M. H. Devoret, RF-driven Josephson bifurcation amplifier for quantum measurement, Phys. Rev. Lett. 93, 207002 (2004).
  9. E. A. Tholén, A. Ergül, E. M. Doherty, F. M. Weber, F. Grégis, and D. B. Haviland, Nonlinearities and parametric amplification in superconducting coplanar waveguide resonators, Appl. Phys. Lett. 90, 253509 (2007).
  10. T. Yamamoto, K. Inomata, M. Watanabe, K. Matsuba, T. Miyazaki, W. D. Oliver, Y. Nakamura, and J. S. Tsai, Flux-driven Josephson parametric amplifier, Appl. Phys. Lett. 93, 042510 (2008).
  11. Y. Asaki, B. Alcalde Pampliega, P. G. Edwards, S. Iguchi, and E. J. Murphy, Astronomical radio interferometry, Nat. Rev. Methods Primers 3, 89 (2023).
  12. M. E. Marhic, P. A. Andrekson, P. Petropoulos, S. Radic, C. Peucheret, and M. Jazayerifar, Fiber optical parametric amplifiers in optical communication systems, Laser Photon. Rev. 9, 50 (2015).
  13. S. V. Dvornikov, A. F. Kryachko, I. A. Velmisov, and D. A. Zatuchny, Amplifiers in Radio Receivers: Characteristics, Operating Principles, and Efficiency, Springer Aerospace Technology (Springer, 2022).
  14. M. Koch, D. M. Mittleman, J. Ornik, and E. Castro-Camus, Terahertz time-domain spectroscopy, Nat. Rev. Methods Primers 3, 48 (2023).
  15. N. Du et al., Search for invisible axion dark matter with the axion dark matter experiment, Phys. Rev. Lett. 120, 151301 (2018).
  16. A. M. Zagoskin, E. Il’ichev, M. W. McCutcheon, J. F. Young, and F. Nori, Controlled generation of squeezed States of microwave radiation in a superconducting resonant circuit, Phys. Rev. Lett. 101, 253602 (2008).
  17. Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, Observation of nonlocal interference in separated photon channels, Phys. Rev. Lett. 65, 321 (1990).
  18. E. M. Nagasako, S. J. Bentley, R. W. Boyd, and G. S. Agarwal, Nonclassical two-photon interferometry and lithography with high-gain parametric amplifiers, Phys. Rev. A 64, 043802 (2001).
  19. M. A. Castellanos-Beltran, K. D. Irwin, G. C. Hilton, L. R. Vale, and K. W. Lehnert, Amplification and squeezing of quantum noise with a tunable Josephson metamaterial, Nat. Phys. 4, 929 (2008).
  20. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  21. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  22. S. D. Bass and M. Doser, Quantum sensing for particle physics, Nat. Rev. Phys. 6, 329 (2024).
  23. C. Macklin, K. O’Brien, D. Hover, M. E. Schwartz, V. Bolkhovsky, X. Zhang, W. D. Oliver, and I. Siddiqi, A near-quantum-limited Josephson traveling-wave parametric amplifier, Science 350, 307 (2015).
  24. L. Amico, A. Osterloh, and F. Cataliotti, Quantum many particle systems in ring-shaped optical lattices, Phys. Rev. Lett. 95, 063201 (2005).
  25. L. Amico, et al., Roadmap on atomtronics: State of the art and perspective, AVS Quantum Sci. 3, 039201 (2021).
  26. 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).
  27. 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).
  28. 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).
  29. 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).
  30. C. Ryu, E. C. Samson, and M. G. Boshier, Quantum interference of currents in an atomtronic SQUID, Nat. Commun. 11, 3338 (2020).
  31. C.-C. Chien, S. Peotta, and M. Di Ventra, Quantum transport in ultracold atoms, Nat. Phys. 11, 998 (2015).
  32. S. Krinner, T. Esslinger, and J.-P. Brantut, Two-terminal transport measurements with cold atoms, J. Phys.: Condens. Matter 29, 343003 (2017).
  33. 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).
  34. F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, Josephson junction arrays with Bose-Einstein condensates, Science 293, 843 (2001).
  35. 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).
  36. L. J. LeBlanc, A. B. Bardon, J. McKeever, M. H. T. Extavour, D. Jervis, J. H. Thywissen, F. Piazza, and A. Smerzi, Dynamics of a tunable superfluid junction, Phys. Rev. Lett. 106, 025302 (2011).
  37. G. Spagnolli, G. Semeghini, L. Masi, G. Ferioli, A. Trenkwalder, S. Coop, M. Landini, L. Pezzè, G. Modugno, M. Inguscio, A. Smerzi, and M. Fattori, Crossing over from attractive to repulsive interactions in a tunneling Bosonic Josephson junction, Phys. Rev. Lett. 118, 230403 (2017).
  38. M. Pigneur, T. Berrada, M. Bonneau, T. Schumm, E. Demler, and J. Schmiedmayer, Relaxation to a phase-locked equilibrium state in a one-dimensional Bosonic Josephson junction, Phys. Rev. Lett. 120, 173601 (2018).
  39. 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).
  40. 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).
  41. 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).
  42. 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.
  43. K. S. Gan, V. P. Singh, L. Amico, and R. Dumke, Josephson dynamics in 2D ring-shaped condensates, arXiv:2509.00533.
  44. 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).
  45. E. Rydow, V. P. Singh, A. Beregi, E. Chang, L. Mathey, C. J. Foot, and S. Sunami, Observation of a bilayer superfluid with interlayer coherence, Nat. Commun. 16, 7201 (2025).
  46. 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).
  47. 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).
  48. 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).
  49. 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).
  50. S. Giovanazzi, A. Smerzi, and S. Fantoni, Josephson effects in dilute Bose-Einstein condensates, Phys. Rev. Lett. 84, 4521 (2000).
  51. S. Jährling, V. P. Singh, and L. Mathey, Designing atomtronic circuits via superfluid dynamics, Phys. Rev. Res. 7, 033112 (2025).
  52. B. Zhu, V. P. Singh, J. Okamoto, and L. Mathey, Dynamical control of the conductivity of an atomic Josephson junction, Phys. Rev. Res. 3, 013111 (2021).
  53. S. Kohler and F. Sols, Chemical potential standard for atomic Bose–Einstein condensates, New J. Phys. 5, 94 (2003).
  54. A. Eckardt, T. Jinasundera, C. Weiss, and M. Holthaus, Analog of photon-assisted tunneling in a Bose-Einstein condensate, Phys. Rev. Lett. 95, 200401 (2005).
  55. J. Grond, T. Betz, U. Hohenester, N. J. Mauser, J. Schmiedmayer, and T. Schumm, The Shapiro effect in atomchip-based bosonic Josephson junctions, New J. Phys. 13, 065026 (2011).
  56. N. Pradhan, R. Kanamoto, M. Bhattacharya, and P. K. Mishra, Fractional Shapiro steps in a cavity-coupled Josephson ring condensate, Phys. Rev. Res. 7, 043188 (2025).
  57. V. P. Singh, J. Polo, L. Mathey, and L. Amico, Shapiro steps in driven atomic Josephson junctions, Phys. Rev. Lett. 133, 093401 (2024).
  58. S. Shapiro, Josephson currents in superconducting tunneling: The effect of microwaves and other observations, Phys. Rev. Lett. 11, 80 (1963).
  59. C. C. Grimes and S. Shapiro, Millimeter-wave mixing with Josephson junctions, Phys. Rev. 169, 397 (1968).
  60. 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).
  61. 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).
  62. P. 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).
  63. A. Polkovnikov, Phase space representation of quantum dynamics, Ann. Phys. (NY) 325, 1790 (2010).
  64. V. P. Singh, W. Weimer, K. Morgener, J. Siegl, K. Hueck, N. Luick, H. Moritz, and L. Mathey, Probing superfluidity of Bose-Einstein condensates via laser stirring, Phys. Rev. A 93, 023634 (2016).
  65. V. P. Singh and L. Mathey, Sound propagation in a two-dimensional Bose gas across the superfluid transition, Phys. Rev. Res. 2, 023336 (2020).
  66. N. Prokof'ev, O. Ruebenacker, and B. Svistunov, Critical point of a weakly interacting two-dimensional Bose gas, Phys. Rev. Lett. 87, 270402 (2001).
  67. N. Prokof'ev and B. Svistunov, Two-dimensional weakly interacting Bose gas in the fluctuation region, Phys. Rev. A 66, 043608 (2002).
  68. See Supplemental Material at http://link.aps.org/supplemental/10.1103/7s1n-ddp9 for the driven junction spectrum, the current-chemical potential characteristic, and the driven RSJ circuit model, which includes Refs. [57, 72].
  69. D. Sheng, A. R. Perry, S. P. Krzyzewski, S. Geller, J. Kitching, and S. Knappe, A microfabricated optically-pumped magnetic gradiometer, Appl. Phys. Lett. 110, 031106 (2017).
  70. J. Javor, Z. Yao, M. Imboden, D. K. Campbell, and D. J. Bishop, Analysis of a Casimir-driven parametric amplifier with resilience to Casimir pull-in for MEMS single-point magnetic gradiometry, Microsyst. Nanoeng. 7, 73 (2021).
  71. K. Somiya, K. Suzuki, S. Otabe, and K. Harada, Intracavity signal amplification system for next-generation gravitational-wave detectors, Phys. Rev. D 107, 122005 (2023).
  72. 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).

Outline

Information

Phys. Rev. Research 8, L012067– Published 20 March, 2026
  • Received 2 April 2025
  • Accepted 11 February 2026
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