Atomic motion dynamics during structural changes or chemical reactions have been visualized by pico- and femtosecond pulsed electron beams via ultrafast electron diffraction and microscopy. Imaging the even faster dynamics of electrons in atoms, molecules, and solids requires electron pulses with subfemtosecond durations. We demonstrate here the all-optical generation of trains of attosecond free-electron pulses. The concept is based on the periodic energy modulation of a pulsed electron beam via an inelastic interaction, with the ponderomotive potential of an optical traveling wave generated by two femtosecond laser pulses at different frequencies in vacuum. The subsequent dispersive propagation leads to a compression of the electrons and the formation of ultrashort pulses. The longitudinal phase space evolution of the electrons after compression is mapped by a second phase-locked interaction. The comparison of measured and calculated spectrograms reveals the attosecond temporal structure of the compressed electron pulse trains with individual pulse durations of less than 300 as. This technique can be utilized for tailoring and initial characterization of suboptical-cycle free-electron pulses at high repetition rates for stroboscopic time-resolved experiments with subfemtosecond time resolution.

In the early days of quantum mechanics Kapitza and Dirac predicted that matter waves would scatter o the optical intensity grating formed by two counter-propagating light waves 1 . This interaction, driven by the ponderomotive potential of the optical standing wave, was both studied theoretically and demonstrated experimentally for atoms 2 and electrons 3-5 . In the original version of the experiment 1,5 , only the transverse momentum of particles was varied, but their energy and longitudinal momentum remained unchanged after the interaction. Here, we report on the generalization of the Kapitza-Dirac e ect. We demonstrate that the energy of sub-relativistic electrons is strongly modulated on the few-femtosecond timescale via the interaction with a travelling wave created in vacuum by two colliding laser pulses at di erent frequencies. This e ect extends the possibilities of temporal control of freely propagating particles with coherent light and can serve the attosecond ballistic bunching of electrons 6 , or for the acceleration of neutral atoms or molecules by light.Depending on the scattering regime, the interaction between electrons and the ponderomotive potential of an optical standing wave can be described both quantum mechanically (Kapitza-Dirac effect 7-9 ) or classically 8,10 . In the quantum picture, the matter wave coherently diffracts on the periodic potential of the two colliding optical waves with wavevectors k and −k and identical frequency ω, leading to observation of a series of diffraction peaks separated by two photon recoils 2hk (Raman-Nath regime 5,7 ) or an individual diffraction peak (Bragg regime 8,11 ). From the point of view of energy and momentum conservation, a diffracted particle simultaneously absorbs a photon from the first wave and emits a photon to the second wave via stimulated Compton scattering. The strength of the interaction is proportional to the light intensity (density of photons) of the optical standing wave.From the classical perspective describing an incoherent scattering regime 4,8,10 , the periodic ponderomotive potential of the optical standing wave U p = e 2 |E 0 | 2 /(m 0 ω 2 ) cos 2 (k · r), where e is electron charge, m 0 is electron mass, r is position vector and E 0 is the field amplitude of each wave, leads to scattering of electrons due to the spatial dependence of the transverse ponderomotive force F p = −∇U p .

The temporal resolution of ultrafast electron diffraction and microscopy experiments is currently limited by the available experimental techniques for the generation and characterization of electron bunches with single femtosecond or attosecond durations. Here, we present proof of principle experiments of an optical gating concept for free electrons via direct time-domain visualization of the sub-optical cycle energy and transverse momentum structure imprinted on the electron beam. We demonstrate a temporal resolution of 1.2±0.3 fs. The scheme is based on the synchronous interaction between electrons and the near-field mode of a dielectric nano-grating excited by a femtosecond laser pulse with an optical period duration of 6.5 fs. The sub-optical cycle resolution demonstrated here is promising for use in laser-driven streak cameras for attosecond temporal characterization of bunched particle beams as well as time-resolved experiments with free-electron beams.

Dielectric laser acceleration is a versatile scheme to accelerate and control electrons with the help of femtosecond laser pulses in nanophotonic structures. We demonstrate here the generation of a train of electron pulses with individual pulse durations as short as 270±80 attoseconds(FWHM), measured in an indirect fashion, based on two subsequent dielectric laser interaction regions connected by a free-space electron drift section, all on a single photonic chip. In the first interaction region (the modulator), an energy modulation is imprinted on the electron pulse. During free propagation, this energy modulation evolves into a charge density modulation, which we probe in the second interaction region (the analyzer). These results will lead to new ways of probing ultrafast dynamics in matter and are essential for future laser-based particle accelerators on a photonic chip.

The widespread use of high energy particle beams in basic research 1-3 , medicine 4,5 and coherent Xray generation 6 coupled with the large size of modern radio frequency (RF) accelerator devices and facilities has motivated a strong need for alternative accelerators operating in regimes outside of RF. Working at optical frequencies, dielectric laser accelerators (DLAs) -transparent laser-driven nanoscale dielectric structures whose near fields can synchronously accelerate charged particleshave demonstrated high-gradient acceleration with a variety of laser wavelengths, materials, and electron beam parameters 7-11 , potentially enabling miniaturized accelerators and table-top coherent x-ray sources 9,12 . To realize a useful (i.e. scalable) DLA, crucial developments have remained: concatenation of components including sustained phase synchronicity to reach arbitrary final energies as well as deflection and focusing elements to keep the beam well collimated along the design axis. Here, all of these elements are demonstrated with a subrelativistic electron beam. In particular, by creating two interaction regions via illumination of a nanograting with two spatio-temporally separated pulsed laser beams, we demonstrate a phase-controlled doubling of electron energy gain from 0.7 to 1.4 keV (2.5% to 5% of the initial beam energy) and through use of a chirped grating geometry, we overcome the dephasing limit of 25 keV electrons, increasing their energy gains to a laser power limited 10% of their initial energy. Further, optically-driven transverse focusing of the electron beam with focal lengths below 200 μm is achieved via a parabolic grating geometry. These results lay the cornerstone for future miniaturized phase synchronous vacuum-structure-based accelerators. DLAs are enticing insofar as they can provide high energy particle beams using the well-established principle of phase-synchronous acceleration in vacuum 1,2,13,14 , but with a smaller footprint, higher acceleration gradient and beam properties distinct from those available via microwave acceleration 9 . In dielectric laser acceleration, electrons traverse nanostructured dielectric geometries, gaining energy via interaction with laser-induced accelerating fields 9,15-19 . These fields are generated by imprinting a periodic spatial modulation to the perpendicularly incident laser wavefront that matches the periodicity of the structure and leads to optical near-field modes travelling along the structure surface (see Figure 1). Electrons with a velocity matching the phase velocity of one of the surface modes are accelerated if injected at an appropriate phase. Notably, DLAs are based on a vacuum scheme, similar to RF accelerators, and the imparted energy gain scales linearly with the incident optical field strength, presenting clear advantages over nonlinear acceleration schemes requiring matter 20-21 . Due to the linear interaction of the laser-induced fields with the accelerated electrons, the imparted energy gain can be extended by adding sequential interactio...