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Nonlinear-optical quantum control of free-electron matter waves

Nature Physics volume 19, pages 1350–1354 (2023)Cite this article

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Abstract

Although electrons and photons are the most widely researched elementary particles, their interactions outside of the confines of a material are not yet fully explored. Here, we report the use of nonlinear-optical two-photon transitions for the quantum-coherent control of a free-electron matter wave in free space. We superimpose an electron beam with two crossed laser beams of different photon energies for non-linear Compton scattering. At suitable angle combinations, the electron energy spectrum becomes modulated into discrete energy sidebands with thousands of interference maxima. We explain our observations by the cascaded addition and subtraction of two-photon pairs under three-body conservation of energy and momentum. Calculations reveal that the electron matter wave converts into pulses of few-attosecond duration. These results show the general importance of matter wave coherences in scattering phenomena and provide a way for investigating and creating quantum correlations and entanglement between massive and massless elementary particles without the need for a classical coupling construct.

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Fig. 1: Experimental concept and results.
Fig. 2: Conservation of energy and momentum and cascaded two-photon transitions.
Fig. 3: Coherent energy broadening in stronger laser fields.
Fig. 4: Spatiotemporal quantum simulations and compression of electron pulses in the time domain.

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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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Acknowledgements

This research was supported by the German Research Foundation via SFB 1432 and by the European Union’s Horizon 2020 research and innovation programme via Marie Skłodowska-Curie grant 713694.

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Author notes

  1. These authors contributed equally: Maxim Tsarev, Johannes W. Thurner.

Authors and Affiliations

  1. Fachbereich Physik, Universität Konstanz, Konstanz, Germany

    Maxim Tsarev, Johannes W. Thurner & Peter Baum

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  1. Maxim Tsarev
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Contributions

P.B. and M.T. conceived the experiment. J.W.T. and M.T. performed the experiments and analysed the data. M.T. performed the simulations. P.B. and M.T. wrote the manuscript with help of all coauthors.

Corresponding author

Correspondence to Peter Baum.

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Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Theoretical spectrum in comparison to the experiment.

The simulated spectrum (blue) leading to the few-attosecond pulses of Fig. 4 compares well to the measured spectrum (black) as replotted from Fig. 3a. The apparent noise in the simulations are coherent effects. A slight asymmetry in the experiment (energy gain region are more intense than energy loss regions) is related to the energy-sensitivity of the camera’s phosphor screen, a quantity that has not been corrected for in the experiment.

Extended Data Fig. 2 Broadband electron energy spectroscopy from concatenated measurements.

The color curves show the individual electron energy ranges and the color arrows denote the measured energy shifts. Together, these results produce the spectrum of Fig. 3a.

Extended Data Fig. 3 Correction of long-term drifts in the high-resolution sideband spectra of Fig. 3.

The four columns correspond to four different central energies of the magnetic spectrometer (0 eV, 100 eV, 1000 eV and 1500 eV). a, Directly averaged images without drift correction. The sidebands are visible at 0-eV central energy (high electron flux) but not at the other energies the due to fluctuations and drifts. b, Fourier-transform images of the vertically-binned spectrometer images in dependency on image number (top to down, first to last). A spike in the spectrum is present in almost all of the images. c, Spectral amplitude (black curve) and spectral phase (red curve). The peak and the linear phase dependency demonstrate the presence of a trustworthy signal. d, Final spectrometer images after drift correction and averaging. e, Resulting sideband patterns. The arrows indicate the corresponding axes for absolute count rate comparison. The resulting sideband contrast is ~25%, limited by the apparatus function width (compare Fig. 1c).

Source data

Figs. 1–4

Data points as depicted.

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Tsarev, M., Thurner, J.W. & Baum, P. Nonlinear-optical quantum control of free-electron matter waves. Nat. Phys. 19, 1350–1354 (2023). https://doi.org/10.1038/s41567-023-02092-6

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