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Coherent interaction between free electrons and a photonic cavity


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.

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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.


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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




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.

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The authors declare no competing interests.

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

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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.

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

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