Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

You are viewing this page in draft mode.

Coherent interaction between free electrons and a photonic cavity

Abstract

Advances in the research of interactions between ultrafast free electrons and light have introduced a previously unknown kind of quantum matter, quantum free-electron wavepackets1,2,3,4,5. So far, studies of the interactions of cavity-confined light with quantum matter have focused on bound electron systems, such as atoms, quantum dots and quantum circuits, which are considerably limited by their fixed energy states, spectral range and selection rules. By contrast, quantum free-electron wavepackets have no such limits, but so far no experiment has shown the influence of a photonic cavity on quantum free-electron wavepackets. Here we develop a platform for multidimensional nanoscale imaging and spectroscopy of free-electron interactions with photonic cavities. We directly measure the cavity-photon lifetime via a coherent free-electron probe and observe an enhancement of more than an order of magnitude in the interaction strength relative to previous experiments of electron–photon interactions. Our free-electron probe resolves the spatiotemporal and energy–momentum information of the interaction. The quantum nature of the electrons is verified by spatially mapping Rabi oscillations of the electron spectrum. The interactions between free electrons and cavity photons could enable low-dose, ultrafast electron microscopy of soft matter or other beam-sensitive materials. Such interactions may also open paths towards using free electrons for quantum information processing and quantum sensing. Future studies could achieve free-electron strong coupling6,7, photon quantum state synthesis8 and quantum nonlinear phenomena such as cavity electro-optomechanics9.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Quantum interaction of free electrons with a photonic cavity in the UTEM.
Fig. 2: Reconstruction of band structure and direct imaging of the Bloch modes of the photonic crystal.
Fig. 3: Mapping of quantum coherent electron–light interactions in a photonic-crystal cavity mode, showing a spatial-analogue of Rabi oscillations.
Fig. 4: Direct measurement of photon lifetime and dynamics using a free electron.
Fig. 5: Enhanced interaction of electrons with picojoule laser pulses in a photonic crystal cavity, and possible applications in quantum state synthesis and ultrafast electron microscopy of sensitive materials.

Data availablity

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

References

  1. 1.

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

    ADS  CAS  PubMed  Google Scholar 

  2. 2.

    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  PubMed  Google Scholar 

  3. 3.

    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  CAS  Google Scholar 

  4. 4.

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

    ADS  CAS  PubMed  Google Scholar 

  5. 5.

    Piazza, L. U. C. A. et al. Simultaneous observation of the quantization and the interference pattern of a plasmonic near-field. Nat. Commun. 6, 6407 (2015).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  6. 6.

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

    ADS  CAS  PubMed  Google Scholar 

  7. 7.

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

    ADS  Google Scholar 

  8. 8.

    Brattke, S., Varcoe, B. T. H. & Walther, H. Generation of photon number states on demand via cavity quantum electrodynamics. Phys. Rev. Lett. 86, 3534–3537 (2001).

    ADS  CAS  PubMed  Google Scholar 

  9. 9.

    Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    ADS  Google Scholar 

  10. 10.

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

    ADS  CAS  Google Scholar 

  11. 11.

    Morimoto, Y. & Baum, P. Diffraction and microscopy with attosecond electron pulse trains. Nat. Phys. 14, 252–256 (2018).

    CAS  Google Scholar 

  12. 12.

    Kozák, M., Schönenberger, N. & Hommelhoff, P. Ponderomotive generation and detection of attosecond free-electron pulse trains. Phys. Rev. Lett. 120, 103203 (2018).

    ADS  PubMed  Google Scholar 

  13. 13.

    Vanacore, G. M. et al. Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields. Nat. Mater. 18, 573–579 (2019).

    ADS  CAS  PubMed  Google Scholar 

  14. 14.

    Mechel, C. et al. Imaging the collapse of electron wave-functions: the relation to plasmonic losses. In CLEO: QELS_Fundamental Science FF3M.6 (OSA Publishing, 2019).

  15. 15.

    Friedman, A., Gover, A., Kurizki, G., Ruschin, S. & Yariv, A. Spontaneous and stimulated emission from quasifree electrons. Rev. Mod. Phys. 60, 471–535 (1988).

    ADS  CAS  Google Scholar 

  16. 16.

    Garcıía de Abajo, F. J. Multiple excitation of confined graphene plasmons by single free electrons. ACS Nano 7, 11409–11419 (2013).

    PubMed  Google Scholar 

  17. 17.

    Schächter, L. Beam-Wave Interaction in Periodic and Quasi-Periodic Structures (Springer, 2013).

  18. 18.

    Roques-Carmes, C., Rivera, N., Joannopoulos, J. D., Soljačić, M. & Kaminer, I. Nonperturbative quantum electrodynamics in the Cherenkov effect. Phys. Rev. X 8, 041013 (2018).

    Google Scholar 

  19. 19.

    Rivera, N., Wong, L. J., Joannopoulos, J. D., Soljačić, M. & Kaminer, I. Light emission based on nanophotonic vacuum forces. Nat. Phys. 15, 1284–1289 (2019).

    CAS  Google Scholar 

  20. 20.

    Wang K. et al. Transmission nearfield optical microscopy (TNOM) of photonic crystal Bloch modes. In CLEO: QELS_Fundamental Science JTh5B.9 (OSA Publishing, 2019).

  21. 21.

    Wang, K. et al. Coherent interaction between free electrons and cavity photons. Preprint at https://arxiv.org/abs/1908.06206 (2019).

  22. 22.

    Pomarico, E. et al. meV resolution in laser-assisted energy-filtered transmission electron microscopy. ACS Photonics 5, 759–764 (2018).

    CAS  Google Scholar 

  23. 23.

    Vanacore, G. M. et al. Attosecond coherent control of free-electron wave functions using semi-infinite light fields. Nat. Commun. 9, 2694 (2018); correction 10, 1069 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  24. 24.

    Park, S. T., Kwon, O.-H. & Zewail, A. H. Chirped imaging pulses in four-dimensional electron microscopy: femtosecond pulsed hole burning. New J. Phys. 14, 053046 (2012).

    ADS  Google Scholar 

  25. 25.

    Kfir, O. et al. Controlling free electrons with optical whispering-gallery modes. Nature https://doi.org/10.1038/s41586-020-2320-y (2020).

  26. 26.

    Liu, H., Baskin, J. S. & Zewail, A. H. Infrared PINEM developed by diffraction in 4D UEM. Proc. Natl Acad. Sci. USA 113, 2041–2046 (2016).

    ADS  CAS  PubMed  Google Scholar 

  27. 27.

    Lummen, T. T. et al. Imaging and controlling plasmonic interference fields at buried interfaces. Nat. Commun. 7, 13156 (2016).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  28. 28.

    Rotenberg, N. & Kuipers, L. Mapping nanoscale light fields. Nat. Photonics 8, 919–926 (2014).

    ADS  CAS  Google Scholar 

  29. 29.

    VandenBussche, E. J. & Flannigan, D. J. Reducing radiation damage in soft matter with femtosecond-timed single-electron packets. Nano Lett. 19, 6687–6694 (2019).

    ADS  CAS  PubMed  Google Scholar 

  30. 30.

    Cognée, K. G. et al. Mapping complex mode volumes with cavity perturbation theory. Optica 6, 269–273 (2019).

    ADS  Google Scholar 

  31. 31.

    Benz, F. et al. Single-molecule optomechanics in “picocavities”. Science 354, 726–729 (2016).

    ADS  CAS  PubMed  Google Scholar 

  32. 32.

    Nehemia, S. et al. Observation of the stimulated quantum Cherenkov effect. Preprint at https://arxiv.org/abs/1909.00757 (2019).

  33. 33.

    Carmon, T. & Vahala, K. J. Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 GHz frequency. Phys. Rev. Lett. 98, 123901 (2007).

    ADS  PubMed  Google Scholar 

  34. 34.

    Reinhardt, O., Mechel, C., Lynch, M. & Kaminer, I. Free electron qubits. In CLEO: QELS_Fundamental Science FF1F.6 (OSA Publishing, 2019).

  35. 35.

    Flannigan, D. J. & Lindenberg, A. M. Atomic-scale imaging of ultrafast materials dynamics. MRS Bull. 43, 485–490 (2018).

    Google Scholar 

  36. 36.

    Madan, I. et al. Holographic imaging of electromagnetic fields via electron–light quantum interference. Sci. Adv. 5, eaav8358 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  37. 37.

    Bartal, G. et al. Brillouin zone spectroscopy of nonlinear photonic lattices. Phys. Rev. Lett. 94, 163902 (2005).

    ADS  PubMed  Google Scholar 

  38. 38.

    Mandelik, D., Eisenberg, H. S., Silberberg, Y., Morandotti, R. & Aitchison, J. S. Band-gap structure of waveguide arrays and excitation of Floquet–Bloch solitons. Phys. Rev. Lett. 90, 053902 (2003).

    ADS  CAS  PubMed  Google Scholar 

  39. 39.

    Abashin, M. et al. Near-field characterization of propagating optical modes in photonic crystal waveguides. Opt. Express 14, 1643–1657 (2006).

    ADS  PubMed  Google Scholar 

  40. 40.

    Engelen, R. J. P. et al. Local probing of Bloch mode dispersion in a photonic crystal waveguide. Opt. Express 13, 4457–4464 (2005).

    ADS  PubMed  Google Scholar 

  41. 41.

    Sapienza, R. et al. Deep-subwavelength imaging of the modal dispersion of light. Nat. Mater. 11, 781–787 (2012).

    ADS  CAS  PubMed  Google Scholar 

  42. 42.

    Peng, S. et al. Probing the band structure of topological silicon photonic lattices in the visible spectrum. Phys. Rev. Lett. 122, 117401 (2019).

    ADS  CAS  PubMed  Google Scholar 

  43. 43.

    Adamo, G. et al. Light well: a tunable free-electron light source on a chip. Phys. Rev. Lett. 103, 113901 (2009).

    ADS  CAS  PubMed  Google Scholar 

  44. 44.

    Sannomiya, T., Saito, H., Junesch, J. & Yamamoto, N. Coupling of plasmonic nanopore pairs: facing dipoles attract each other. Light Sci. Appl. 5, e16146 (2016).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  45. 45.

    Stockman, M. I., Kling, M. F., Kleineberg, U. & Krausz, F. Attosecond nanoplasmonic-field microscope. Nat. Photonics 1, 539–544 (2007).

    ADS  CAS  Google Scholar 

  46. 46.

    Man, M. K. L. et al. Imaging the motion of electrons across semiconductor heterojunctions. Nat. Nanotechnol. 12, 36–40 (2017).

    ADS  CAS  PubMed  Google Scholar 

  47. 47.

    Petek, H. & Ogawa, S. Femtosecond time-resolved two-photon photoemission studies of electron dynamics in metals. Prog. Surf. Sci. 56, 239–310 (1997).

    ADS  CAS  Google Scholar 

  48. 48.

    Kubo, A. et al. Femtosecond imaging of surface plasmon dynamics in a nanostructured silver film. Nano Lett. 5, 1123–1127 (2005).

    ADS  CAS  PubMed  Google Scholar 

  49. 49.

    Spektor, G. et al. Revealing the subfemtosecond dynamics of orbital angular momentum in nanoplasmonic vortices. Science 355, 1187–1191 (2017).

    ADS  CAS  PubMed  Google Scholar 

  50. 50.

    Hyun, J. K., Couillard, M., Rajendran, P., Liddell, C. M. & Muller, D. A. Measuring far-ultraviolet whispering gallery modes with high energy electrons. Appl. Phys. Lett. 93, 243106 (2008).

    ADS  Google Scholar 

  51. 51.

    Cha, J. J. et al. Mapping local optical densities of states in silicon photonic structures with nanoscale electron spectroscopy. Phys. Rev. B 81, 113102 (2010).

    ADS  Google Scholar 

  52. 52.

    Tarhan, İ. İ. & Watson, G. H. Photonic band structure of fcc colloidal crystals. Phys. Rev. Lett. 76, 315–318 (1996).

    ADS  CAS  PubMed  Google Scholar 

  53. 53.

    Honda, M. & Yamamoto, N. High-Q band edge mode of plasmonic crystals studied by cathodoluminescence. Appl. Phys. Lett. 104, 081112 (2014).

    ADS  Google Scholar 

  54. 54.

    Brenny, B. J. M., Beggs, D. M., van der Wel, R. E. C., Kuipers, L. & Polman, A. Near-infrared spectroscopic cathodoluminescence imaging polarimetry on silicon photonic crystal waveguides. ACS Photonics 3, 2112–2121 (2016).

    CAS  Google Scholar 

  55. 55.

    Meuret, S. et al. Complementary cathodoluminescence lifetime imaging configurations in a scanning electron microscope. Ultramicroscopy 197, 28–38 (2019).

    CAS  PubMed  Google Scholar 

  56. 56.

    Yamamoto, N. Development of high-resolution cathodoluminescence system for STEM and application to plasmonic nanostructures. Microscopy 65, 282–295 (2016).

    CAS  PubMed  Google Scholar 

  57. 57.

    Takeuchi, K. & Yamamoto, N. Visualization of surface plasmon polariton waves in two-dimensional plasmonic crystal by cathodoluminescence. Opt. Express 19, 12365–12374 (2011).

    ADS  CAS  PubMed  Google Scholar 

  58. 58.

    Sola Garcia, M., Schilder, N., Meuret, S., Coenen, T. & Polman, A. Time-, and phase-resolved cathodoluminescence spectroscopy. In Q-sort International Conference on Quantum Imaging and Electron Beam Shaping 87–88 (2019).

  59. 59.

    Dani, K. Imaging the motion of charge with time-resolved photoemission electron microscopy. In CLEO: QELS_Fundamental Science FW4M.1 (OSA Publishing, 2019).

Download references

Acknowledgements

The research was supported by the ERC starting grant NanoEP 851780 and the Israel Science Foundation grants 3334/19 and 831/19. K.W. is partially supported by a fellowship from the Lady Davis Foundation. S.T. acknowledges support by the Adams Fellowship Program of the Israel Academy of Science and Humanities. I.K. acknowledges the support of the Azrieli Faculty Fellowship. The experiments were performed on the UTEM of the AdQuanta group of I.K., which is installed in the electron microscopy center (MIKA) of the Department of Materials Science and Engineering at the Technion. We thank IDES Ltd and especially S. T. Park for support, advice and discussions. We are grateful to Y. Yang, M. Soljačić, S. G. Johnson, J. D. Joannopoulos and M. Segev for discussions. I.K. wholeheartedly acknowledges the support of R. Magid and B. Magid, whose donation made the purchase of the UTEM possible; without their help, all the experiments presented here would not have been possible.

Author information

Affiliations

Authors

Contributions

K.W., R.D., M.S. and Y.K. carried out the experiments. A.B.H., O.R. and S.T. developed the quantum description. K.W. produced the figures and proposed and implemented the simulations and the data analysis. I.K. conceived the research. All authors provided substantial input to all aspects of the project and to the writing of the paper.

Corresponding author

Correspondence to Ido Kaminer.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Albert Polman and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Ultrafast TEM for multidimensional spectroscopy (space, momentum, energy, polarization and time).

a, Electron microscopy images of a photonic-crystal membrane used for proof-of-concept demonstrations throughout this work. Imaging of matter and light fields with the electron energy filter disabled (left) and enabled (right). The middle plot shows a typical EELS; energy-filtered electrons used for imaging are marked by the blue shaded area. Scale bar, 300 nm. b, Multiple EELS over a range of sample tilt angles, showing the angle-resolving capability of the technique; the bottom plane displays an angle-resolved EELS map assembled from individual spectra. c, EELS map showing the capability of mapping the electron–photon interaction for a range of wavelengths. d, Snapshots showing the capability of imaging excitations of different incident light polarizations. e, Multiple EELS showing the femtosecond time resolution of the interaction; the bottom plane displays a time-resolved EELS map assembled from individual spectra.

Extended Data Fig. 2 Comparison between simulations and measurements of photonic-crystal band stuctures and images of Bloch modes, also showing the polarization control of Bloch modes.

a, Simulated band structure (upper panel) by the FDTD method (see Methods) matching the measured band structure (lower panel; same as Fig. 2a). b, Illustration of the photonic crystal on a 200-nm-thick Si3N4 membrane. c, Measured (top) and FDTD-simulated (bottom) photonic-crystal Bloch mode images rotating with the polarization direction (double arrows) at normal incidence and 730 nm wavelength (points 1 and 6 in a). d, Simulated images (top) of photonic-crystal Bloch modes corresponding to experimental ones (lower panel; same as Fig. 2c), where \(\overrightarrow{{\bf{E}}}\) is the electric field of the light and \(\hat{{\bf{v}}}\) is the unit vector of the electron velocity. Scale bars, 300 nm.

Extended Data Fig. 3 EELS alignment and reconstruction of the photonic-crystal band structure from a series of EELS measurements.

a, Example of an EELS map before (left) and after (right) alignment of the zero-loss peak (after normalizing the total probability to 1). The drift of the spectra along the x axis may occur because of magnetic fluctuations, and it was corrected by tracking the position of the zero-loss peak in each spectrum. b, Examples of EELS maps as a function of angle, collected at excitation wavelengths of 895 nm, 900 nm, 905 nm and 910 nm, showing that the location of a resonance peak shifts from ~12° to ~17°. The double arrows indicate the integration energy range used to extract the signal, which was chosen to exclude the contribution from the zero-loss peak and was defined as twice the FWHM of the zero-loss peak. c, Curves showing the electron–photon interaction probability as a function of incident angle, obtained from the integration of the EELS angle maps along the energy axis. The triangles indicate the peak shift as a function of wavelength. d, Band structure reconstructed from a series of measurements. The dashed box indicates the pixels shown in the other panels. e, Artefacts in the measured photonic-crystal band structure. The polarization impurity in the laser pulse excitation causes a partial mix of the TM and TE bands. The dashed boxes indicate artefacts in each polarization. The TM (pink) and TE (green) band structures are equivalent to the data presented in Fig. 2a. To illustrate that the artefacts stem from mixed polarization, we overlaid the TE bands (light green) on the TM bands in the left panel. The regions (A1–A3) where the light green mixes with pink indicate the existence of TE polarization in the TM band structure. Similar regions (A4–A6) were also found in the TE band structure.

Extended Data Fig. 4 Image post-processing revealing the optical-field distribution of a single photonic-crystal unit cell.

a, Raw image captured by the camera in greyscale. b, Black and white image binarized by adaptive thresholding, showing the features of the etched holes in the photonic-crystal membrane. c, The photonic-crystal holes are recognized by machine vision using the circular Hough transform. d, Calculation of the geometric distortion. The control points in the red grids are generated from the recognized hole centres. The green lines indicate the control point pairs used for image registration. e, Aligned image recovered from the geometric distortion. f, Cropped image. g, Contrast adjustment on selected image areas: recovery of the field amplitude by normalizing the electron current in the Si3N4 membrane relative to the holes.

Supplementary information

Supplementary Information

This file contains Supplementary Notes 1-7 and References.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wang, K., Dahan, R., Shentcis, M. et al. Coherent interaction between free electrons and a photonic cavity. Nature 582, 50–54 (2020). https://doi.org/10.1038/s41586-020-2321-x

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing