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Free-electron quantum optics

Nature Physics volume 21, pages 193–200 (2025)Cite this article

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Abstract

Recent theoretical and experimental breakthroughs have given rise to the emerging field of free-electron quantum optics, reshaping the understanding of free-electron physics. Traditionally rooted in classical electrodynamics, this field now reveals quantum-mechanical features that necessitate the frameworks of quantum electrodynamics and quantum optics. This shift compels a re-evaluation of well-established areas, bringing quantum-mechanical corrections to accelerator science and to electron-radiation phenomena. Simultaneously, the ability to shape single-electron wavefunctions opens new possibilities in microscopy and spectroscopy. These developments are primarily driven by innovations in electron microscopy and its intersection with laser science, where laser-driven electron modulation substantially influences quantum electron interactions with light and matter. In this Perspective, we review these developments, highlighting the current challenges and future opportunities. We explore the role of the free electron as a quantum resource, complementing conventional two-level systems and harmonic oscillators. In the coming years, free electrons may offer new modalities for reading and writing quantum information on ultrafast timescales, performing quantum-state tomography, and ultrafast quantum gates on the atomic scale.

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Fig. 1: The triangle of interactions in free-electron quantum optics.
Fig. 2: The electron microscope as a quantum-optical lab.
Fig. 3: The free electron can create and measure quantum correlations.

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References

  1. García de Abajo, F. J. Optical excitations in electron microscopy. Rev. Mod. Phys. 82, 209–275 (2010).

    ADS  MATH  Google Scholar 

  2. Roques-Carmes, C. et al. Free-electron–light interactions in nanophotonics. Appl. Phys. Rev. 10, 011303 (2023).

    ADS  Google Scholar 

  3. Baum, P. & Zewail, A. H. Attosecond electron pulses for 4D diffraction and microscopy. Proc. Natl Acad. Sci. USA 104, 18409–18414 (2007).

    ADS  MATH  Google Scholar 

  4. Barwick, B., Flannigan, D. J. & Zewail, A. H. Photon-induced near-field electron microscopy. Nature 462, 902–906 (2009).

    ADS  Google Scholar 

  5. García de Abajo, F. J., Asenjo-Garcia, A. & Kociak, M. Multiphoton absorption and emission by interaction of swift electrons with evanescent light fields. Nano Lett. 10, 1859–1863 (2010).

    ADS  MATH  Google Scholar 

  6. Park, S. T., Lin, M. & Zewail, A. H. Photon-induced near-field electron microscopy (PINEM): theoretical and experimental. New J. Phys. 12, 123028 (2010).

    ADS  Google Scholar 

  7. Aidelsburger, M. et al. Single-electron pulses for ultrafast diffraction. Proc. Natl Acad. Sci. USA 107, 19714–19719 (2010).

    ADS  Google Scholar 

  8. Lichte, H. & Lehmann, M. Electron holography—basics and applications. Rep. Prog. Phys. 71, 016102 (2007).

    ADS  MATH  Google Scholar 

  9. McMorran, B. J. & Cronin, A. D. An electron Talbot interferometer. New J. Phys. 11, 033021 (2009).

    ADS  MATH  Google Scholar 

  10. Feist, A. et al. Quantum coherent optical phase modulation in an ultrafast transmission electron microscope. Nature 521, 200–203 (2015).

    ADS  MATH  Google Scholar 

  11. Bucher, T. et al. Free-electron Ramsey-type interferometry for enhanced amplitude and phase imaging of nearfields. Sci. Adv. 9, eadi5729 (2023).

    MATH  Google Scholar 

  12. Mohler, K. J. et al. Ultrafast electron diffraction from nanophotonic waveforms via dynamical Aharonov–Bohm phases. Sci. Adv. 6, eabc8804 (2020).

    ADS  Google Scholar 

  13. Turner, A. E., Johnson, C. W., Kruit, P. & McMorran, B. J. Interaction-free measurement with electrons. Phys. Rev. Lett. 127, 110401 (2021).

    ADS  Google Scholar 

  14. Priebe, K. E. et al. Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy. Nat. Photon. 11, 793–797 (2017).

    ADS  MATH  Google Scholar 

  15. Dahan, R. et al. Imprinting the quantum statistics of photons on free electrons. Science 373, eabj7128 (2021).

    MATH  Google Scholar 

  16. Kaminer, I. et al. Quantum Cerenkov radiation: spectral cutoffs and the role of spin and orbital angular momentum. Phys. Rev. X 6, 011006 (2016).

    MATH  Google Scholar 

  17. Karnieli, A., Rivera, N., Arie, A. & Kaminer, I. The coherence of light is fundamentally tied to the quantum coherence of the emitting particle. Sci. Adv. 7, eabf8096 (2021).

    ADS  Google Scholar 

  18. Kfir, O., Di Giulio, V., de Abajo, F. J. G. & Ropers, C. Optical coherence transfer mediated by free electrons. Sci. Adv. 7, eabf6380 (2021).

    ADS  Google Scholar 

  19. Ben Hayun, A. et al. Shaping quantum photonic states using free electrons. Sci. Adv. 7, eabe4270 (2021).

    ADS  Google Scholar 

  20. Tsesses, S., Bartal, G. & Kaminer, I. Light generation via quantum interaction of electrons with periodic nanostructures. Phys. Rev. A 95, 013832 (2017).

    ADS  Google Scholar 

  21. Giulio, V. D. & de Abajo, F. J. G. Optical-cavity mode squeezing by free electrons. Nanophotonics 11, 4659–4670 (2022).

    MATH  Google Scholar 

  22. Dahan, R. et al. Creation of optical cat and GKP states using shaped free electrons. Phys. Rev. X 13, 031001 (2023).

    MATH  Google Scholar 

  23. Bucher, T. et al. Coherently amplified ultrafast imaging using a free-electron interferometer. Nat. Photon. 18, 809–815 (2024).

    MATH  Google Scholar 

  24. Madan, I. et al. Charge dynamics electron microscopy: nanoscale imaging of femtosecond plasma dynamics. ACS Nano 17, 3657–3665 (2023).

    MATH  Google Scholar 

  25. Yannai, M. et al. Ultrafast electron microscopy of nanoscale charge dynamics in semiconductors. ACS Nano 17, 3645–3656 (2023).

    MATH  Google Scholar 

  26. Gover, A. & Yariv, A. Free-electron–bound-electron resonant interaction. Phys. Rev. Lett. 124, 064801 (2020).

    ADS  MATH  Google Scholar 

  27. Rätzel, D., Hartley, D., Schwartz, O. & Haslinger, P. Controlling quantum systems with modulated electron beams. Phys. Rev. Res. 3, 023247 (2021).

    Google Scholar 

  28. Ruimy, R., Gorlach, A., Mechel, C., Rivera, N. & Kaminer, I. Toward atomic-resolution quantum measurements with coherently shaped free electrons. Phys. Rev. Lett. 126, 233403 (2021).

    ADS  MATH  Google Scholar 

  29. Zhao, Z., Sun, X.-Q. & Fan, S. Quantum entanglement and modulation enhancement of free-electron–bound-electron interaction. Phys. Rev. Lett. 126, 233402 (2021).

    ADS  MathSciNet  MATH  Google Scholar 

  30. García de Abajo, F. J., Dias, E. J. C. & Di Giulio, V. Complete excitation of discrete quantum systems by single free electrons. Phys. Rev. Lett. 129, 093401 (2022).

    ADS  MATH  Google Scholar 

  31. Karnieli, A. et al. Quantum sensing of strongly coupled light–matter systems using free electrons. Sci. Adv. 9, eadd2349 (2023).

    MATH  Google Scholar 

  32. Lim, J., Kumar, S., Ang, Y. S., Ang, L. K. & Wong, L. J. Quantum interference between fundamentally different processes is enabled by shaped input wavefunctions. Adv. Sci. 10, 2205750 (2023).

    MATH  Google Scholar 

  33. Schattschneider, P. & Löffler, S. Entanglement and decoherence in electron microscopy. Ultramicroscopy 190, 39–44 (2018).

    MATH  Google Scholar 

  34. Mechel, C. et al. Quantum correlations in electron microscopy. Optica 8, 70–78 (2021).

    ADS  MATH  Google Scholar 

  35. Feist, A. et al. Cavity-mediated electron-photon pairs. Science 377, 777–780 (2022).

    ADS  MATH  Google Scholar 

  36. Adiv, Y. et al. Observation of 2D Cherenkov radiation. Phys. Rev. X 13, 011002 (2023).

    MATH  Google Scholar 

  37. Huang, G., Engelsen, N. J., Kfir, O., Ropers, C. & Kippenberg, T. J. Electron–photon quantum state heralding using photonic integrated circuits. PRX Quantum 4, 020351 (2023).

    ADS  Google Scholar 

  38. Karnieli, A. & Fan, S. Jaynes–Cummings interaction between low-energy free electrons and cavity photons. Sci. Adv. 9, eadh2425 (2023).

    MATH  Google Scholar 

  39. Karnieli, A. et al. Universal and ultrafast quantum computation based on free-electron–polariton blockade. PRX Quantum 5, 010339 (2024).

    ADS  MATH  Google Scholar 

  40. Baranes, G. et al. Free-electron interactions with photonic GKP states: universal control and quantum error correction. Phys. Rev. Res. 5, 043271 (2023).

    MATH  Google Scholar 

  41. Baranes, G., Ruimy, R., Gorlach, A. & Kaminer, I. Free electrons can induce entanglement between photons. npj Quantum Inf. 8, 32 (2022).

    ADS  Google Scholar 

  42. Jaynes, E. T. & Cummings, F. W. Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51, 89–109 (1963).

    MATH  Google Scholar 

  43. Kfir, O. Entanglements of electrons and cavity photons in the strong-coupling regime. Phys. Rev. Lett. 123, 103602 (2019).

    ADS  MATH  Google Scholar 

  44. Giulio, V. D., Kociak, M. & de Abajo, F. J. G. Probing quantum optical excitations with fast electrons. Optica 6, 1524–1534 (2019).

    ADS  MATH  Google Scholar 

  45. Meuret, S. et al. Photon bunching in cathodoluminescence. Phys. Rev. Lett. 114, 197401 (2015).

    ADS  MATH  Google Scholar 

  46. Sola-Garcia, M. et al. Photon statistics of incoherent cathodoluminescence with continuous and pulsed electron beams. ACS Photon. 8, 916–925 (2021).

    MATH  Google Scholar 

  47. Fiedler, S. et al. Sub-to-super-Poissonian photon statistics in cathodoluminescence of color center ensembles in isolated diamond crystals. Nanophotonics 12, 2231–2237 (2023).

    MATH  Google Scholar 

  48. Arredondo, J. A. & Fernandez-Dominguez, A. I. Electron-assisted probing of polaritonic light-matter states. Nanophotonics 13, 2015–2027 (2024).

    ADS  MATH  Google Scholar 

  49. Taleb, M. Charting the exciton–polariton landscape of WSe2 thin flakes by cathodoluminescence spectroscopy. Adv. Photon. Res. 3, 2100124 (2021).

    MATH  Google Scholar 

  50. Shiloh, R., Lereah, Y., Lilach, Y. & Arie, A. Sculpturing the electron wave function using nanoscale phase masks. Ultramicroscopy 144, 26–31 (2014).

    Google Scholar 

  51. Verbeeck, J. et al. Demonstration of a 2×2 programmable phase plate for electrons. Ultramicroscopy 190, 58–65 (2018).

    MATH  Google Scholar 

  52. Madan, I. et al. Ultrafast transverse modulation of free electrons by interaction with shaped optical fields. ACS Photon. 9, 3215–3224 (2022).

    Google Scholar 

  53. Tsesses, S. et al. Tunable photon-induced spatial modulation of free electrons. Nat. Mater. 22, 345–352 (2023).

    ADS  Google Scholar 

  54. Garcia de Abajo, F. J. & Konecna, A. Optical modulation of electron beams in free space. Phys. Rev. Lett. 126, 123901 (2021).

    ADS  MATH  Google Scholar 

  55. Mihaila, M. C. C. et al. Transverse electron-beam shaping with light. Phys. Rev. X. 12, 031043 (2022).

    MATH  Google Scholar 

  56. Reinhardt, O., Mechel, C., Lynch, M. & Kaminer, I. Free-electron qubits. Ann. Phys. 533, 2000254 (2021).

    MATH  Google Scholar 

  57. Tsarev, M. V., Ryabov, A. & Baum, P. Free-electron qubits and maximum-contrast attosecond pulses via temporal Talbot revivals. Phys. Rev. Res. 3, 043033 (2021).

    Google Scholar 

  58. Ebel, S. & Talebi, N. Inelastic electron scattering at a single-beam structured light wave. Comm. Phys. 6, 179 (2023).

    ADS  MATH  Google Scholar 

  59. Tsarev, M. et al. Nonlinear-optical quantum control of free-electron matter waves. Nat. Phys. 19, 1350–1354 (2023).

    MATH  Google Scholar 

  60. Albert, V. V., Covey, J. P. & Preskill, J. Robust encoding of a qubit in a molecule. Phys. Rev. X 10, 031050 (2020).

    MATH  Google Scholar 

  61. Löffler, S. Unitary two-state quantum operators realized by quadrupole fields in the electron microscope. Ultramicroscopy 234, 113456 (2022).

    MATH  Google Scholar 

  62. Zimmermann, R., Seidling, M. & Hommelhoff, P. Charged particle guiding and beam splitting with auto-ponderomotive potentials on a chip. Nat. Commun. 12, 390 (2021).

    ADS  Google Scholar 

  63. Grillo, V. et al. Measuring the orbital angular momentum spectrum of an electron beam. Nat. Commun. 8, 15536 (2017).

    ADS  MATH  Google Scholar 

  64. Bendaña, X., Polman, A. & García de Abajo, F. J. Single-photon generation by electron beams. Nano Lett. 11, 5099–5103 (2011).

    ADS  MATH  Google Scholar 

  65. Kling, P. et al. What defines the quantum regime of the free-electron laser? New J. Phys. 17, 123019 (2015).

    ADS  MATH  Google Scholar 

  66. Huang, S. et al. Quantum recoil in free-electron interactions with atomic lattices. Nat. Photon. 17, 224–230 (2023).

    ADS  MATH  Google Scholar 

  67. Eldar, M., Chen, Z., Pan, Y. & Krüger, M. Self-trapping of slow electrons in the energy domain. Phys. Rev. Lett. 132, 035001 (2024).

    ADS  MATH  Google Scholar 

  68. Talebi, N. Strong interaction of slow electrons with near-field light visited from first principles. Phys. Rev. Lett. 125, 080401 (2020).

    ADS  MATH  Google Scholar 

  69. Dahan, R. et al. Resonant phase-matching between a light wave and a free-electron wavefunction. Nat. Phys. 16, 1123–1131 (2020).

    MATH  Google Scholar 

  70. Reinhardt, O. & Kaminer, I. Theory of shaping electron wavepackets with light. ACS Photon. 7, 2859–2870 (2020).

    MATH  Google Scholar 

  71. Yalunin, S. V., Feist, A. & Ropers, C. Tailored high-contrast attosecond electron pulses for coherent excitation and scattering. Phys. Rev. Res. 3, L032036 (2021).

    Google Scholar 

  72. Henke, J.-W. et al. Integrated photonics enables continuous-beam electron phase modulation. Nature 600, 653–658 (2021).

    ADS  MATH  Google Scholar 

  73. Bezard, M. et al. High-efficiency coupling of free electrons to sub-λ3 modal volume, high-Q photonic cavities. ACS Nano 18, 10417–11042 (2024).

    MATH  Google Scholar 

  74. Karnieli, A. et al. Strong coupling and single-photon nonlinearity in free-electron quantum optics. ACS Photon. 11, 3401 (2024).

    MATH  Google Scholar 

  75. Kruit, P. et al. Designs for a quantum electron microscope. Ultramicroscopy 164, 31–45 (2016).

    Google Scholar 

  76. Seidling, M. et al. Resonating electrostatically guided electrons. Phys. Rev. Lett. 132, 255001 (2024).

    Google Scholar 

  77. Varkentina, N. et al. Cathodoluminescence excitation spectroscopy: nanoscale imaging of excitation pathways. Sci. Adv. 8, eabq4947 (2022).

    ADS  MATH  Google Scholar 

  78. Ruimy, R., Gorlach, A., Baranes, G. & Kaminer, I. Superradiant electron energy loss spectroscopy. Nano Lett. 23, 779–787 (2023).

    ADS  Google Scholar 

  79. Meier, S., Heimerl, J. & Hommelhoff, P. Few-electron correlations after ultrafast photoemission from nanometric needle tips. Nat. Phys. 19, 1402–1409 (2023).

    Google Scholar 

  80. Haindl, R. et al. Coulomb-correlated electron number states in a transmission electron microscope beam. Nat. Phys. 19, 1410–1417 (2023).

    MATH  Google Scholar 

  81. Kumar, S. et al. Strongly correlated multielectron bunches from interaction with quantum light. Sci. Adv. 10, adm9563 (2024).

    Google Scholar 

  82. Okamoto, H. & Nagatani, Y. Entanglement-assisted electron microscopy based on a flux qubit. Appl. Phys. Lett. 104, 062604 (2014).

    ADS  MATH  Google Scholar 

  83. Karnieli, A., Rivera, N., Arie, A. & Kaminer, I. Superradiance and subradiance due to quantum interference of entangled free electrons. Phys. Rev. Lett. 127, 060403 (2021).

    ADS  MathSciNet  Google Scholar 

  84. García de Abajo, F. J. & Di Giulio, V. Optical excitations with electron beams: challenges and opportunities. ACS Photon. 8, 945–974 (2021).

    MATH  Google Scholar 

  85. Koppell, S. A., Israel, Y., Bowman, A. J., Klopfer, B. B. & Kasevich, M. A. Transmission electron microscopy at the quantum limit. Appl. Phys. Lett. 120, 190502 (2022).

    Google Scholar 

  86. Wang, K. et al. Coherent interaction between free electrons and a photonic cavity. Nature 582, 50–54 (2020).

    ADS  MATH  Google Scholar 

  87. Kfir, O. et al. Controlling free electrons with optical whispering-gallery modes. Nature 582, 46–49 (2020).

    ADS  MATH  Google Scholar 

  88. Kurman, Y. et al. Spatiotemporal imaging of 2D polariton wave packet dynamics using free electrons. Science 372, 1181–1186 (2021).

    ADS  MATH  Google Scholar 

  89. Nabben, D., Kuttruff, J., Stolz, L., Ryabov, A. & Baum, P. Attosecond electron microscopy of sub-cycle optical dynamics. Nature 619, 63–67 (2023).

    ADS  Google Scholar 

  90. Gaida, J. H. et al. Attosecond electron microscopy by free-electron homodyne detection. Nat. Photon. 18, 509–515 (2024).

    ADS  Google Scholar 

  91. Potapov, P. L., Lichte, H., Verbeeck, J. & van Dyck, D. Experiments on inelastic electron holography. Ultramicroscopy 106, 1012–1018 (2006).

    Google Scholar 

  92. Verbeeck, J., Tian, H. & Schattschneider, P. Production and application of electron vortex beams. Nature 467, 301–304 (2010).

    ADS  MATH  Google Scholar 

  93. Guzzinati, G. et al. Probing the symmetry of the potential of localized surface plasmon resonances with phase-shaped electron beams. Nat. Commun. 8, 14999 (2017).

    ADS  MATH  Google Scholar 

  94. Gaida, J. H. et al. Lorentz microscopy of optical fields. Nat. Commun. 14, 6545 (2023).

    ADS  MATH  Google Scholar 

  95. Gorlach, A. et al. Ultrafast non-destructive measurement of the quantum state of light using free electrons. Preprint at https://arxiv.org/abs/2012.12069 (2020).

  96. Christopher, J. et al. Electron-driven photon sources for correlative electron–photon spectroscopy with electron microscopes. Nanophotonics 9, 4381–4406 (2020).

    MATH  Google Scholar 

  97. Taleb, M., Hentschel, M., Rossnagel, K., Giessen, H. & Talebi, N. Phase-locked photon–electron interaction without a laser. Nat. Phys. 19, 869–876 (2023).

    Google Scholar 

  98. Giulio, V. D. et al. Toward optimum coupling between free electrons and confined optical modes. ACS. Nano 18, 14255 (2024).

    MATH  Google Scholar 

  99. Shiloh, R., Chlouba, T. & Hommelhoff, P. Quantum-coherent light–electron interaction in a scanning electron microscope. Phys. Rev. Lett. 128, 235301 (2022).

    ADS  MATH  Google Scholar 

  100. Sorensen, A. & Molmer, K. Quantum computation with ions in thermal motion. Phys. Rev. Lett. 82, 1971 (1999).

    ADS  MATH  Google Scholar 

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  1. These authors contributed equally: Ron Ruimy, Aviv Karnieli.

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  1. Technion – Israel Institute of Technology, Solid State Institute, Haifa, Israel

    Ron Ruimy, Aviv Karnieli & Ido Kaminer

  2. E. L. Ginzton Laboratories, Stanford University, Stanford, CA, USA

    Aviv Karnieli

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  1. Ron Ruimy
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  2. Aviv Karnieli
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Ruimy, R., Karnieli, A. & Kaminer, I. Free-electron quantum optics. Nat. Phys. 21, 193–200 (2025). https://doi.org/10.1038/s41567-024-02743-2

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