Abstract

The state vector representing a quantum system acquires a phase factor following an adiabatic evolution along a closed trajectory in phase space. This is the traditional example of a geometric phase, or Pancharatnam–Berry phase, a concept that has now been generalized beyond cyclic adiabatic evolutions to include generalized quantum measurements, and that has been experimentally measured in a variety of physical systems. However, a clear description of the relationship between the emergence of a geometric phase and the effects of a series of generalized quantum measurements on a quantum system has not yet been provided. Here we report that a sequence of weak measurements with continuously variable measurement strengths in a quantum optics experiment conclusively reveals that the quantum measurement back-action is the source of the geometric phase—that is, the stronger a quantum measurement, the larger the accumulated geometric phase. We furthermore find that in the limit of strong (projective) measurement there is a direct connection between the geometric phase and the sequential weak value, ordinarily associated with a series of weak quantum measurements.

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The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

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Journal peer review information: Nature Physics thanks Andrew Jordan and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Acknowledgements

This work was supported by the KIST institutional programmes (project nos 2E29580 and 2E27800-18-P044), by the ICT R&D programme of MSIP/IITP (grant no. B0101-16-1355) and by the National Research Foundation of Korea (grant nos 2016R1A2A1A05005202 and 2016R1A4A1008978). Y.K. acknowledges support from the Global PhD Fellowship by the National Research Foundation of Korea (grant no. 2015H1A2A1033028).

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Author notes

  1. These authors contributed equally: Young-Wook Cho, Yosep Kim.

Affiliations

  1. Center for Quantum information, Korea Institute of Science and Technology, Seoul, Korea

    • Young-Wook Cho
    • , Yeon-Ho Choi
    • , Yong-Su Kim
    • , Sang-Wook Han
    • , Sang-Yun Lee
    •  & Sung Moon
  2. Department of Physics, Pohang University of Science and Technology, Pohang, Korea

    • Yosep Kim
    •  & Yoon-Ho Kim
  3. Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea

    • Yeon-Ho Choi
    • , Yong-Su Kim
    •  & Sung Moon

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Contributions

Y.-W.C and Y.-H.K planned and supervised the research. Y.-W.C designed the experiment. Y.K., Y.-H.C., Y.-W.C. and Y.-S.K. performed the experiment. Y.-W.C., Y.K. and Y.-H.K. carried out the theoretical calculations, analysed data and discussed the results. Y.-S.K., Y.-H.C. S.-W.H., S.-Y.L. and S.M. contributed to the analysis and discussion of the results. Y.-W.C, Y.K. and Y.-H.K wrote the manuscript with input from all authors.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to Young-Wook Cho or Yoon-Ho Kim.

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https://doi.org/10.1038/s41567-019-0482-z