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High-harmonic generation driven by quantum light

Nature Physics volume 19, pages 1689–1696 (2023)Cite this article

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Abstract

High-harmonic generation (HHG) is an extreme nonlinear process in which intense pulses of light drive matter to emit high harmonics of the driving frequency, reaching the extreme ultraviolet and X-ray spectral ranges. So far, HHG has always been generated by intense laser pulses that are well described as a classical electromagnetic field. However, the role of the quantum state of light in non-perturbative interactions of intense light with matter has remained unexplored. Here we show that the defining spectral characteristics of HHG, such as the plateau and cutoff, are sensitive to the quantum state of light. While coherent and Fock light states induce the established HHG cutoff law, thermal and squeezed states substantially surpass it, extending the cutoff compared with a coherent light state of the same intensity. Shaping the quantum state of light thus enables the production of far higher harmonics. We develop the theory of extreme nonlinear optics driven by squeezed light, and more generally by arbitrary quantum states of light, introducing the quantum state of the driving field as a degree of freedom.

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Fig. 1: An extended spectral cutoff for HHG driven by quantum light states.
Fig. 2: Interactions of bound electrons with quantum light.
Fig. 3: Spectra of HHG for different driving light states.
Fig. 4: The physical origin of the extended cutoffs for thermal and squeezed light states.
Fig. 5: Simulations of the high-harmonic spectra for different driving intensities.

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Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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The code is available from the corresponding author upon reasonable request.

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Acknowledgements

We acknowledge insightful discussions on related topics with A. Pizzi, R. Ruimy and J. Sloan. The work was supported by the Israel Science Foundation (ISF) under grant no. 830/19, by the Goldman Frontiers in Discovery Grant from the Michigan-Israel Partnership for Research and by the Helen Diller Quantum Center of Technion. The work was also partially supported by European Research Center (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant no. 819440 TIMP).

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Author notes

  1. These authors contributed equally: Alexey Gorlach, Matan Even Tzur.

Authors and Affiliations

  1. Department of Electrical and Computer Engineering and Solid State Institute, Technion–Israel Institute of Technology, Haifa, Israel

    Alexey Gorlach, Michael Birk & Ido Kaminer

  2. Department of Physics and Solid State Institute, Technion–Israel Institute of Technology, Haifa, Israel

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

  3. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Nicholas Rivera

  4. Department of Physics, Harvard University, Cambridge, MA, USA

    Nicholas Rivera

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Contributions

All authors contributed substantially to this work. A.G., M.E.T., I.K. and N.R. developed the initial theoretical ideas. A.G. and M.E.T. performed the numerical calculations. I.K., O.C., M.K., N.R. and M.B. made significant contributions in the development of theoretical concepts and ideas. I.K. and O.C. supervised the project.

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Correspondence to Ido Kaminer.

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Gorlach, A., Tzur, M.E., Birk, M. et al. High-harmonic generation driven by quantum light. Nat. Phys. 19, 1689–1696 (2023). https://doi.org/10.1038/s41567-023-02127-y

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