"Demonstrating Electron-heralded Photon State Preparation & Electron-Photon Entanglement"

Abstract:

Extending inelastic electron-light scattering to the single-electron single-photon regime has generated considerable interest, with theoretical studies promising the generation [1] and probing [2] of quantum states of light as well as entanglement-based quantum-enhanced sensing [3]. The advent of event-based electron detection, enabling electron-photon coincidence measurements [4,5], as well as a boost in the underlying interaction strength through velocity phase matching and resonant field enhancement [6,7], have brought these proposals within reach of state-of-the-art experiments. The preparation of nonclassical states of light and the demonstration of electron-photon entanglement are two critical milestones in the development of free-electron quantum optics.
In this contribution, we present the experimental realisation of these cornerstones: The demonstration of electron-heralded photon number state generation and the observation of free-electron-photon entanglement. For the former, we place integrated optical waveguide structures inside a transmission electron microscope (TEM) to enhance the electron interaction with a single optical mode, creating electron-photon pair states [4]. Using time- and energy-resolved detection of both particles, we trace the resulting correlation between energy-loss electrons and photon generation. Extending the photon detection setup by a second detector, we study the photon statistics heralded by such loss-electrons in a Hanbury Brown and Twiss (HBT) setup and observe an anti-bunching that verifies the generation of non-classical photon number states [8]. The underlying inelastic electron-light scattering is expected to induce entanglement, which can be investigated using a quantum eraser-type scheme involving the electron position and photon polarisation [9,10]. In the experiments, we pass two partial electron beams, generated in a coherent superposition utilizing an amplitude grating, near the two edges of a sub-micron-sized, metal-coated glass prism. At these edges, the electrons can spontaneously emit photons with a polarisation tied to the electron path [11]. Observing the interference of the recombined electron beams in coincidence with measurements of the photon polarisation in different bases, we experimentally implement a state tomography of the complete electron-photon quantum state and find a violation of the Peres-Horodecki entanglement criterion by more than 7 standard deviations. This constitutes a first unequivocal demonstration of free-electron-photon entanglement [11,12].
In summary, we discuss the preparation of electron-heralded photon number states and the verification of electron-photon entanglement. These results have significant implications for the development of free-electron quantum optics, demonstrating the feasibility of electron-driven sources of quantum light and paving the way to quantum-enhanced sensing in electron microscopy based on photon-mediated electron entanglement.

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[6] J.-W. Henke et al., Nature 600 (2021), 653-658

[7] K. Wang et al., Nature 582 (2020), 50-54

[8] G. Arend et al., arXiv:2409.11300 (2024), preprint

[9] J.-W. Henke, H. Jeng & C. Ropers, Phys. Rev. A 111 (2025), 012610

[10] E. Kazakevich, H. Aharon & O. Kfir, Phys. Rev. Res. 6 (2024), 043033

[11] J.-W. Henke, H. Jeng, M. Sivis & C. Ropers, arXiv:2504.13047 (2025), preprint

[12] A. Preimesberger et al., arXiv:2504.13163 (2025), preprint