Coherent manipulation of quantum systems with light is expected to be a cornerstone of future information and communication technology, including quantum computation and cryptography1. The transfer of an optical phase onto a quantum wavefunction is a defining aspect of coherent interactions and forms the basis of quantum state preparation, synchronization and metrology. Light-phase-modulated electron states near atoms and molecules are essential for the techniques of attosecond science, including the generation of extreme-ultraviolet pulses and orbital tomography2,3. In contrast, the quantum-coherent phase-modulation of energetic free-electron beams has not been demonstrated, although it promises direct access to ultrafast imaging and spectroscopy with tailored electron pulses on the attosecond scale. Here we demonstrate the coherent quantum state manipulation of free-electron populations in an electron microscope beam. We employ the interaction of ultrashort electron pulses with optical near-fields4,5,6,7,8,9 to induce Rabi oscillations in the populations of electron momentum states, observed as a function of the optical driving field. Excellent agreement with the scaling of an equal-Rabi multilevel quantum ladder is obtained10, representing the observation of a light-driven ‘quantum walk’5 coherently reshaping electron density in momentum space11. We note that, after the interaction, the optically generated superposition of momentum states evolves into a train of attosecond electron pulses. Our results reveal the potential of quantum control for the precision structuring of electron densities, with possible applications ranging from ultrafast electron spectroscopy and microscopy to accelerator science and free-electron lasers.
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We thank M. Sivis and B. Schröder for help with sample preparation. We also thank our colleagues within the Göttingen UTEM initiative (C. Jooß, M. Münzenberg, K. Samwer, M. Seibt, C.A. Volkert). This work was supported by the Deutsche Forschungsgemeinschaft (DFG-SFB 1073/project A05), the VolkswagenStiftung, and the Lower Saxony Ministry of Science and Culture. We thank JEOL Ltd and JEOL Germany for their continuing support during the development of the Göttingen Ultrafast Transmission Electron Microscope.
The authors declare no competing financial interests.
Extended data figures and tables
Pulses from an amplified femtosecond (fs) laser system, at bottom left, are split into two optical beams. One of them is frequency-doubled in a β-barium borate (BBO) crystal and, after separation from the fundamental beam, focused (lens with numerical aperture 0.015, 50 cm focal length) onto the tungsten needle emitter (W tip) for the generation of electron probe pulses. The second beam (pump beam) is temporally stretched, attenuated and focused (lens with numerical aperture 0.014, 20 cm focal length) onto the sample within the TEM (angle of incidence, 55°). Relative timing between the electron probe and laser pump pulse is controlled by an optical delay stage. Optically-induced changes of the population of electron momentum states are recorded with an electron energy spectrometer. See Methods for details.
a, Raster scan of the optically-induced electron energy gain and loss probability, characterized by the spectral cutoff (top panel) and the sideband populations of the zero loss peak (middle) and the second photon order (bottom). The field-dependent electron energy spectra shown in Fig. 2 of the main text were recorded at an x position indicated by the black line at the tip surface. A slow sample drift results in a scanning artefact in the y direction (jagged edge of the tip). For the results reported in the main text, a drift correction in the y direction was applied (see Methods section ‘Data analysis and drift correction’). b, TEM image of gold tip. Red rectangle, scanning area displayed in a. c, Electron energy-loss spectra recorded along x = 0 with varying distance from the tip surface.
a, Differential electron energy-loss spectra as function of time delay (zero loss peak of width 1.3 eV subtracted; the colour scale shows the relative change of spectral density). b, Relative total scattering amplitude as function of time delay (inset, relative shift of photon sidebands with respect to zero loss peak). c, Energy- and time-resolved structure of the electron pulse (the colour scale shows the normalized electron density).
Example of electron energy spectrum (black dots) showing a number of photon sidebands and a weak low-loss plasmon contribution. Lines show fitted function used to extract sideband populations (blue) and the plasmon band (orange).
a, Effect of electron beam size (top) and laser pulse duration (bottom) on the visibility of the Rabi oscillations in the order |N| = 1. For increasing electron beam size and decreasing laser pulse duration, the modulations are strongly damped. The black curves correspond to the experimental situation. b, Occupation probabilities of multiple spectral sidebands. Solid lines, Nth-order Bessel functions. Dashed lines, numerical calculations accounting for temporal and spatial averaging in the experiments.
The influence of the electron beam’s initial energy spread and lateral size on the temporal peak width of the generated pulse train are shown in the upper and lower rows, respectively. a–d, Evolution of the electron density as a function of propagation distance after the interaction with the optical near-field, incoherently averaged over the initial kinetic energy distribution (a, b) or the finite probing-area of the electron beam (c, d). A corresponding line profile at the propagation distance where the electron density peaks are at their maximum and form an attosecond pulse train is shown in e and f. For the experimental parameters used in this work (energy spread ΔE = 0.7 eV FWHM and electron beam radius r = 10 nm), the peak width remains nearly unchanged as compared to the ideal (not averaged) case.
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Feist, A., Echternkamp, K., Schauss, J. et al. Quantum coherent optical phase modulation in an ultrafast transmission electron microscope. Nature 521, 200–203 (2015). https://doi.org/10.1038/nature14463
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