Abstract

A quantum phase transition (QPT) occurs between two competing phases of matter at zero temperature, driven by quantum fluctuations. Although the presence of these fluctuations is well established, they have not been locally imaged in space, and their local dynamics has not been studied so far. We use a scanning superconducting quantum interference device to image quantum fluctuations near the QPT from a superconductor to an insulator. We find fluctuations of the diamagnetic response in both space and time that survive well below the transition temperature, demonstrating their quantum nature. The fluctuations appear as telegraph-like noise with a range of characteristic times and a non-monotonic temperature dependence, revealing unexpected quantum granularity. The lateral dimension of these fluctuations grows towards criticality, offering a new measurable length scale. Our results provide physical insight into the reorganization of phases across a QPT, with implications for any theoretical description. This paves a new route for future quantum information applications.

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Acknowledgements

We are grateful for technical help from I. Volotchenko and E. A. Persky, and for discussions with D. Roditchev. A.K. and B.K. were supported by the European Research Council grant ERC-2014-STG-639792 and the Israel Science Foundation grant ISF-1281/17. A.F. and N.T. acknowledge support from the Israel US bi-national foundation grant no. 2014325. A.K., A.F and B.K acknowledge the COST Action CA16218. B.K. acknowledges the QuantERA ERA-NET Cofund in Quantum Technologies (project no. 731473). T.I.B. acknowledges support by the Russian Science Foundation (project no. 14-22-00143) and by the Consejería de Educación, Cultura y Deporte (Comunidad de Madrid) through the talent attraction programme, ref. 2016-T3/IND-1839.

Author information

Affiliations

  1. Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan, Israel

    • A. Kremen
    • , T. I. Baturina
    • , A. Frydman
    •  & B. Kalisky
  2. Department of Physics, The Ohio State University, Columbus, OH, USA

    • H. Khan
    •  & N. Trivedi
  3. Department of Physics and Astrophysics, University of North Dakota, Grand Forks, ND, USA

    • Y. L. Loh
  4. Institute of Semiconductor Physics, Novosibirsk, Russia

    • T. I. Baturina
  5. Novosibirsk State University, Novosibirsk, Russia

    • T. I. Baturina

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Contributions

A.K. and B.K. designed the experiment and performed the measurements. A.F. initiated the research and participated in experiments. T.I.B. provided the samples and related measurements. H.K., Y.L.L. and N.T. performed the calculations. N.T, A.F. and B.K. prepared the manuscript with input from all co-authors.

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The authors declare no competing interests.

Corresponding authors

Correspondence to A. Frydman or B. Kalisky.

Supplementary information

  1. Supplementary Information

    Supplementary Figures 1–6

  2. Supplementary Video

    Evolution of susceptibility in sample S1 with temperature. Top panel: susceptibility maps at different temperatures in S1. The images, STD and susceptibility signal describe the local evolution of susceptibility as the sample heats slightly above Tc and cooled down again. At T > Tc no diamagnetic response is observed and the image reflects the SQUID noise. At T < Tc the image shows the presence of darker puddles and streaks of weaker superconductivity, which survive well below Tc. Bottom panel, left: standard deviation (STD) versus temperature, extracted from susceptibility maps shown in the top panel. The STD is normalized to the highest value in each curve. Bottom panel, right: susceptibility signal versus temperature. The vertical bars show the range of susceptibility values in each image.

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DOI

https://doi.org/10.1038/s41567-018-0264-z