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

Physical Review Applied

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
  • Editors' Suggestion
  • Open Access
  • Access by Xinjiang University

Digital holographic imaging for free surfaces of superfluid helium

Vitor S. Barroso1,*, Patrik Švančara1,†,‡, Chris Goodwin1, Sreelekshmi C. Ajithkumar2,§, Ilaria Dimina1, Silvia Schiattarella2, Pietro Smaniotto1, Leonardo Solidoro1, Marion Cromb1 et al.

Radivoje Prizia2,∥, Anthony J. Kent2, and Silke Weinfurtner1,3,4

  • 1School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom
  • 2School of Physics and Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom
  • 3Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, United Kingdom
  • 4Photon Science Institute, Alan Turing Building, University of Manchester, Manchester, M13 9PY, United Kingdom

  • *Contact author: vitor.barroso.s@outlook.com
  • †patrik.svancara@neel.cnrs.fr
  • ‡Present address: Institut Néel, CNRS-UGA, 25 avenue des Martyrs, 38042 Grenoble, France.
  • §Present address: Department of Physics, University of Strathclyde, Glasgow, G4 0NG, United Kingdom.
  • ∥Present address: Laboratoire Kastler-Brossel, Sorbonne Université, ENS-Université PSL, CNRS, Collège de France, 4 place Jussieu, 75005 Paris, France.
PDF

Phys. Rev. Applied 26, 014080 – Published 24 July, 2026

DOI: https://doi.org/10.1103/dh9b-k6hm

Abstract

Visualizing the free surface of superfluid helium offers a rare opportunity to explore wave dynamics in the limit of vanishing viscosity. Such measurements are nonetheless challenging due to helium’s low refractive index contrast, restricted optical access to the cryogenic setups required to maintain helium in its superfluid phase, and mechanical vibrations from the various cooling stages. Overcoming these limitations will enable quantitative studies of surface-wave dynamics with applications in fluid mechanics, quantum simulation, and quantum optomechanics. Here, we report an implementation of off-axis digital holography for full-field imaging of the free surface of superfluid He4. We perform noncontact measurements of nanometer- to micrometer-scale interface fluctuations in two cryogenic systems: a traditional helium bath cryostat and a cryogen-free refrigerator. We employ machine-learning-based analysis to isolate noise-driven normal modes and their spatial structure in both systems. This enables reconstruction of the dispersion relation for gravity-capillary waves in macroscopic samples and, for thick films, determination of the film thickness from the measured dispersion, providing a quantitative benchmark for our approach. These proof-of-concept experiments show that digital holography is a powerful and versatile tool for high-resolution, minimally invasive studies of superfluid surfaces, with strong potential for integration into diverse experimental platforms.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (63)

  1. G. V. Kolmakov, P. V. E. McClintock, and S. V. Nazarenko, Capillary turbulence on the surfaces of quantum fluids, Progress in Low Temperature Physics, edited by W. P. Halperin (Elsevier, Amsterdam, 2009), Vol. 16, pp. 203–255.
  2. G. V. Kolmakov, P. V. E. McClintock, and S. V. Nazarenko, Wave turbulence in quantum fluids, Proc. Natl. Acad. Sci. U.S.A. 111, 4727 (2014).
  3. L. V. Abdurakhimov, M. Y. Brazhnikov, I. A. Remizov, and A. A. Levchenko, Observation of wave energy accumulation in the turbulent spectrum of capillary waves on the He-II surface under harmonic pumping, JETP Lett. 91, 271 (2010).
  4. L. Mezhov-Deglin, A. Pel’menev, and A. Levchenko, Kelvin-Helmholtz instability forced by the intensive Faraday waves on the free surface of superfluid He-II, Mater. Lett. 238, 226 (2019).
  5. P. L. Marston and W. M. Fairbank, Evidence of a large superfluid vortex in He4, Phys. Rev. Lett. 39, 1208 (1977).
  6. V. Tsepelin, H. Alles, A. Babkin, R. Jochemsen, A. Y. Parshin, and I. A. Todoshchenko, Morphology and growth kinetics of He3 crystals below 1 mK, J. Low Temp. Phys. 129, 489 (2002).
  7. I. A. Todoshchenko, H. Alles, H. J. Junes, A. Y. Parshin, and V. Tsepelin, Growth dynamics and faceting of He3 crystals, J. Low Temp. Phys. 148, 635 (2007).
  8. J. R. T. Seddon, M. S. Thurlow, M. J. Lees, and P. G. J. Lucas, Quantised vortex line visualisation in superfluid helium using low-temperature optics, Phys. B Condens. Matter 329-333, 220 (2003).
  9. E. Vittoratos, M. W. Cole, and P. P. M. Meincke, Free surface of a rotating HeII film, Can. J. Phys. 51, 2283 (1973).
  10. J. R. T. Seddon, M. S. Thurlow, and P. G. J. Lucas, Quantised vortex visualisation, J. Low Temp. Phys. 138, 499 (2005).
  11. F. Moisy, M. Rabaud, and K. Salsac, A synthetic Schlieren method for the measurement of the topography of a liquid interface, Exp. Fluids 46, 1021 (2009).
  12. R. J. Donnelly and C. F. Barenghi, The observed properties of liquid helium at the saturated vapor pressure, J. Phys. Chem. Ref. Data 27, 1217 (1998).
  13. S. Wildeman, Real-time quantitative Schlieren imaging by fast Fourier demodulation of a checkered backdrop, Exp. Fluids 59, 97 (2018).
  14. P. Švančara, P. Smaniotto, L. Solidoro, J. F. MacDonald, S. Patrick, R. Gregory, C. F. Barenghi, and S. Weinfurtner, Rotating curved spacetime signatures from a giant quantum vortex, Nature (London) 628, 66 (2024).
  15. P. Smaniotto, L. Solidoro, P. Švančara, S. Patrick, M. Richartz, C. F. Barenghi, R. Gregory, and S. Weinfurtner, Black-hole spectroscopy from a giant quantum vortex, arXiv:2502.11209.
  16. L. Yaroslavsky, Digital Holography and Digital Image Processing (Springer, New York, 2013).
  17. P. Picart and J. Li, Digital Holography (ISTE Wiley-ISTE, Newark, 2013).
  18. U. Schnars, C. Falldorf, J. Watson, and W. Jüptner, Digital Holography and Wavefront Sensing (Springer Berlin, Heidelberg, 2014).
  19. B. Bhaduri, C. Edwards, H. Pham, R. Zhou, T. H. Nguyen, L. L. Goddard, and G. Popescu, Diffraction phase microscopy: Principles and applications in materials and life sciences, Adv. Opt. Photon. 6, 57 (2014).
  20. V. S. Barroso, A. Geelmuyden, S. C. Ajithkumar, A. J. Kent, and S. Weinfurtner, Multiplexed digital holography for fluid surface profilometry, Appl. Opt. 62, 7175 (2023).
  21. Z. Huang and L. Cao, Quantitative phase imaging based on holography: Trends and new perspectives, Light Sci. Appl. 13, 145 (2024).
  22. Y. K. Park, C. Depeursinge, and G. Popescu, Quantitative phase imaging in biomedicine, Nat. Photonics 12, 578 (2018).
  23. X. Yu, J. Hong, C. Liu, and M. K. Kim, Review of digital holographic microscopy for three-dimensional profiling and tracking, Opt. Eng. 53, 112306 (2014).
  24. J. Wu, G. Zheng, and L. M. Lee, Optical imaging techniques in microfluidics and their applications, Lab Chip 12, 3566 (2012).
  25. R. Kumar and G. Dwivedi, Emerging scientific and industrial applications of digital holography: An overview, Eng. Res. Express 5, 032005 (2023).
  26. J. Smits, A. P. Mosk, and P. van der Straten, Imaging trapped quantum gases by off-axis holography, Opt. Lett. 45, 981 (2020).
  27. I. Skachko, J. A. Hay, C. O. Goodwin, M. J. Doyle, W. Guo, P. M. Walmsley, and A. I. Golov, Apparatus to visualize flows in superfluid He4 below 1 K, arXiv:2602.21279.
  28. T. Eikelmann, M. Brinkmann, L. Eggers, T. Ulas, D. Imeri, K. Beck, L. J. Irrgang, S. K. Mahato, R. Shah, and R. Riedinger, High-performance imaging in a dilution refrigerator, APL Quantum 3, 026109 (2026).
  29. F. Pobell, Matter and Methods at Low Temperatures, 3rd ed. (Springer Berlin, Heidelberg, 2007).
  30. T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram, Opt. Express 14, 4300 (2006).
  31. G. Whitham, Linear dispersive waves, Linear and Nonlinear Waves (John Wiley & Sons, Hoboken, 1999), Chap. 11, pp. 361–402.
  32. D. J. Bergman, Third sound in superfluid helium films of arbitrary thickness, Phys. Rev. A 3, 2058 (1971).

  33. We obtain the kinematic viscosity of gaseous helium, νg=1.2×10−6 m2/s, as its dynamic viscosity, given by Eq. (2) in [63], divided by its density, calculated from the standard equation of state of an ideal gas.

  34. H. Li, G. C. Linderman, A. Szlam, K. P. Stanton, Y. Kluger, and M. Tygert, Algorithm 971: An implementation of a randomized algorithm for principal component analysis, ACM Trans. Math. Softw. 43, 28 (2017).
  35. C. D. Manning, P. Raghavan, and H. Schütze, Matrix decompositions and latent semantic indexing, in Introduction to Information Retrieval (Cambridge University Press, 2008), pp. 369–384.
  36. S. C. Ajithkumar, V. S. Barroso, P. Švančara, A. J. Kent, and S. Weinfurtner, Optical lever for broadband detection of fluid interface fluctuations, Appl. Opt. 65, 222 (2026).
  37. R. Lake, S. Simbierowicz, P. Krantz, F. Hassani, and J. M. Fink, The Bluefors Dilution Refrigerator as an Integrated Quantum Measurement System, Application Note (Bluefors Oy, Helsinki, Finland, 2021).
  38. J. Smetana, T. Yan, V. Boyer, and D. Martynov, A high-finesse suspended interferometric sensor for macroscopic quantum mechanics with femtometre sensitivity, Sensors 24, 2375 (2024).
  39. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (SPIE Press, Bellingham, 2020).
  40. S. Montresor and P. Picart, Quantitative appraisal for noise reduction in digital holographic phase imaging, Opt. Express 24, 14322 (2016).
  41. F. M. Ellis and L. Li, Quantum swirling of superfluid helium films, Phys. Rev. Lett. 71, 1577 (1993).
  42. Y. P. Sachkou, C. G. Baker, G. I. Harris, O. R. Stockdale, S. Forstner, M. T. Reeves, X. He, D. L. McAuslan, A. S. Bradley, M. J. Davis, and W. P. Bowen, Coherent vortex dynamics in a strongly interacting superfluid on a silicon chip, Science 366, 1480 (2019).
  43. R. Schützhold and W. G. Unruh, Gravity wave analogues of black holes, Phys. Rev. D 66, 044019 (2002).
  44. C. R. D. Bunney, V. S. Barroso, S. Biermann, A. Geelmuyden, C. Gooding, Gégoire Ithier, X. Rojas, J. Louko, and S. Weinfurtner, Third sound detectors in accelerated motion, New J. Phys. 26, 065001 (2024).
  45. F. Ursell, The long-wave paradox in the theory of gravity waves, Math. Proc. Cambridge Philos. Soc. 49, 685 (1953).
  46. Y. L. Sfendla, C. G. Baker, G. I. Harris, L. Tian, R. A. Harrison, and W. P. Bowen, Extreme quantum nonlinearity in superfluid thin-film surface waves, npj Quantum Inf. 7, 62 (2021).
  47. M. T. Reeves, W. W. Wasserman, R. A. Harrison, I. Marinković, N. Luu, A. Sawadsky, Y. L. Sfendla, G. I. Harris, W. P. Bowen, and C. G. Baker, Nonlinear wave dynamics on a chip, Science 390, 371 (2025).
  48. S. Chen, C. Li, C. Ma, T.-C. Poon, and Y. Zhu, Phase sensitivity of off-axis digital holography, Opt. Lett. 43, 4993 (2018).
  49. V. Bianco, P. Memmolo, M. Leo, S. Montresor, C. Distante, M. Paturzo, P. Picart, B. Javidi, and P. Ferraro, Strategies for reducing speckle noise in digital holography, Light Sci. Appl. 7, 48 (2018).
  50. M. R. Sultanova, I. A. Remizov, L. P. Mezhov-Deglin, and A. A. Levchenko, Generation of quantum vortices by waves on the surface of superfluid helium, JETP Lett. 118, 585 (2023).
  51. C. Peretti, J. Vessaire, É. Durozoy, and M. Gibert, Direct visualization of the quantum vortex lattice structure, oscillations, and destabilization in rotating He4, Sci. Adv. 9, eadh2899 (2023).
  52. M. T. Jarema, C. R. D. Bunney, V. S. Barroso, M. Tajik, C. Goodwin, and S. Weinfurtner, Information in quantum field theory simulators: Thin-film superfluid helium, arXiv:2508.07247.
  53. P. Welch, The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms, IEEE Trans. Audio Electroacoust. 15, 70 (1967).
  54. F. J. Harris, On the use of windows for harmonic analysis with the discrete Fourier transform, Proc. IEEE 66, 51 (1978).
  55. E. Cuche, P. Marquet, and C. Depeursinge, Spatial filtering for zero-order and twin-image elimination in digital off-axis holography, Appl. Opt. 39, 4070 (2000).
  56. N. Verrier and M. Atlan, Off-axis digital hologram reconstruction: Some practical considerations, Appl. Opt. 50, H136 (2011).
  57. M. Karray, P. Slangen, and P. Picart, Comparison between digital Fresnel holography and digital image-plane holography: The role of the imaging aperture, Exp. Mech. 52, 1275 (2012).
  58. J.-C. Li, P. Tankam, Z.-J. Peng, and P. Picart, Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification, Opt. Lett. 34, 572 (2009).
  59. J. Li, Z. Peng, and Y. Fu, Diffraction transfer function and its calculation of classic diffraction formula, Opt. Commun. 280, 243 (2007).
  60. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, Scikit-learn: Machine learning in Python, J. Mach. Learn. Res. 12, 2825 (2011); https://jmlr.org/papers/v12/pedregosa11a.html.
  61. C. F. Barenghi, K. R. Sreenivasan, and L. Skrbek, Quantum Turbulence (Cambridge University Press, Cambridge, England, 2023).
  62. K. Penanen and R. E. Packard, A model for third sound attenuation in thick He4 films, J. Low Temp. Phys. 128, 25 (2002).
  63. P. J. Nacher, Viscosity of gaseous He3 and He4 at low temperatures, J. Chem. Phys. 101, 6367 (1994).

Outline

Information

Phys. Rev. Applied 26, 014080– Published 24 July, 2026
  • Received 6 January 2026
  • Revised 22 June 2026
  • Accepted 30 June 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