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Photon-statistics force in ultrafast electron dynamics

Nature Photonics volume 17, pages 501–509 (2023)Cite this article

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Abstract

In strong-field physics and attosecond science, intense light induces ultrafast electron dynamics. Such ultrafast dynamics of electrons in matter is at the core of phenomena such as high-harmonic generation, where these dynamics lead to the emission of extreme-ultraviolet bursts with attosecond duration. So far, all ultrafast dynamics of matter were understood to purely originate from the classical vector potential of the driving light, disregarding the influence of the quantum nature of light. Here we show theoretically that the dynamics of matter driven by bright (intense) light significantly depend on the quantum state of the driving light through its quantum noise, which induces an effective photon-statistics force. To provide a unified framework for the analysis and control over such a force, we extend the strong-field approximation theory to account for non-classical driving light. Our quantum strong-field approximation theory shows that in high-harmonic generation, experimentally feasible squeezing of the driving light can shift and shape electronic trajectories and attosecond pulses at the scale of hundreds of attoseconds. Our work presents a new degree of freedom for attosecond spectroscopy, by relying on non-classical electromagnetic fields, and more generally, introduces a direct connection between attosecond science and quantum optics.

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Fig. 1: Squeezing-dependent generation of attosecond pulses and high-order harmonics.
Fig. 2: Three-step model in a quantized field and the resulting electronic trajectories.
Fig. 3: Dependence of attosecond pulses on squeezing of the driving field.
Fig. 4: Vacuum fluctuations induce yoctosecond time delays in electronic trajectories in HHG.
Fig. 5: Influence of the effective photon-statistics force: Newtonian trajectories.

Data availability

The data supporting the findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The code supporting the findings of this study is available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank the Helen Diller Quantum Center for their support. This work was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (819440-TIMP), and by the Israel Science Foundation (grant no. 1781/18). M.E.T. gratefully acknowledges support from the Council for Higher Education scholarship for excellence in quantum science and technology and the Helen Diller scholarship for excellence in quantum science and technology.

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Author notes

  1. These authors contributed equally: Matan Even Tzur, Michael Birk.

Authors and Affiliations

  1. Solid State Institute and Physics Department, Technion—Israel Institute of Technology, Haifa, Israel

    Matan Even Tzur, Michael Birk, Michael Krüger & Oren Cohen

  2. Solid State Institute and Department of Electrical and Computer Engineering, Technion—Israel Institute of Technology, Haifa, Israel

    Michael Birk, Alexey Gorlach & Ido Kaminer

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  1. Matan Even Tzur
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Contributions

M.E.T. and O.C. initiated this research. A.G. derived the theory presented in Supplementary Section I. M.E.T., M.B. and A.G. derived the theory in Supplementary Section II. M.E.T. and M.B. derived the theory in Supplementary Sections IIIB and IVA. M.E.T. derived the remaining theory, performed the numerical calculations and wrote the first draft of the paper. The project was supervised by O.C., I.K. and M.K. All authors discussed the results and contributed to the writing of the manuscript.

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Correspondence to Matan Even Tzur or Oren Cohen.

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Nature Photonics thanks Maciej Lewenstein, Dejan B. Milosevic and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Sections I–VII and derivations.

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Even Tzur, M., Birk, M., Gorlach, A. et al. Photon-statistics force in ultrafast electron dynamics. Nat. Photon. 17, 501–509 (2023). https://doi.org/10.1038/s41566-023-01209-w

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