Attosecond spectroscopy1-7 can resolve electronic processes directly in time, but a movie-like space-time recording is impeded by the too long wavelength (~100 times larger than atomic distances) or the source-sample entanglement in re-collision techniques [8][9][10][11] . Here we advance attosecond metrology to picometre wavelength and sub-atomic resolution by using free-space electrons instead of higher-harmonic photons 1-7 or re-colliding wavepackets [8][9][10][11] . A beam of 70-keV electrons at 4.5-pm de Broglie wavelength is modulated by the electric field of laser cycles into a sequence of electron pulses with sub-optical-cycle duration. Time-resolved diffraction from crystalline silicon reveals a < 10-as delay of Bragg emission and demonstrates the possibility of analytic attosecond-ångström diffraction. Real-space electron microscopy visualizes with sub-light-cycle resolution how an optical wave propagates in space and time. This unification of attosecond science with electron microscopy and diffraction enables space-time imaging of light-driven processes in the entire range of sample morphologies that electron microscopy can access.Our concepts for generating attosecond electron pulses, direct streaking-oscilloscope characterization, atomic diffraction and proof-of-principle attosecond electron microscopy of electromagnetic fields are depicted in Fig. 1. A femtosecond laser 12 triggers electron emission from a photocathode (yellow) and produces electron pulses of ~1 ps duration at a central energy of E el = 70 keV (ref.13 ). The de Broglie wavelength is λ el ≈ 4.5 pm and spacecharge effects are avoided by using fewer than one electron per pulse at the sample. A first laser beam ('modulation') is used to compress the electron pulse into a sub-cycle pulse train. For this purpose, we let the laser beam and the electron beam intersect at a 50-nm-thick silicon nitride membrane that lets the electrons pass through. The membrane is also transparent to the laser beam (1,030 nm wavelength), but the refractive index of ~2 in combination with thin-layer interferences generates a phase shift between the incoming and outgoing electromagnetic waves. Therefore, the periodic electromagnetic acceleration and deceleration of the propagating electrons in the optical field cycles before and after the membrane do not cancel out after passage through the laser focus, as would happen in free space 13 . In the end, there remains a time-dependent overall momentum kick that is proportional to the change of vector potential at the membrane and therefore dependent on the optical phase. In contrast to metal foils 13,14 , graphite 15 or nanostructures 16 , a dielectric membrane has negligible linear or nonlinear optical absorption and can therefore sustain an extreme level of power and fields, enabling strong/effective compression and metrology.In the experiment, we let the electron beam (0.48 × speed of light) and the laser beam (p-polarized, ~15 mW, peak field ~5 × 10 7 V m -1 ) hit the membrane under 35° and 60° from the surface...

Laser-assisted electron scattering (LAES) in a femtosecond near-infrared intense laser field was observed through the scattering of 1 keV electrons by xenon atoms. The intensities, angular distributions, and laser polarization dependence of the observed LAES signals for the energy gain (+ℏω) and energy loss (-ℏω) processes were interpreted well by numerical simulations. As an application of this femtosecond-LAES process, a new method of time-resolved gas electron diffraction for probing geometrical change of molecules with high precision is proposed.

Attosecond imaging with electron beams can access optical-field-driven electron dynamics in space and time. Here we report first diffraction and microscopy experiments with attosecond electron pulses. We study attosecond-level timing of Bragg-spot emission and visualize light-wave propagation in space and time.