Complex systems in condensed phases involve a multidimensional energy landscape, and knowledge of transitional structures and separation of time scales for atomic movements is critical to understanding their dynamical behavior. Here, we report, using four-dimensional (4D) femtosecond electron diffraction, the visualization of transitional structures from the initial monoclinic to the final tetragonal phase in crystalline vanadium dioxide; the change was initiated by a near-infrared excitation. By revealing the spatiotemporal behavior from all observed Bragg diffractions in 3D, the femtosecond primary vanadium-vanadium bond dilation, the displacements of atoms in picoseconds, and the sound wave shear motion on hundreds of picoseconds were resolved, elucidating the nature of the structural pathways and the nonconcerted mechanism of the transformation.

Short electron pulses are central to time-resolved atomic-scale diffraction and electron microscopy, streak cameras, and free-electron lasers. We demonstrate phase-space control and characterization of 5-picometer electron pulses using few-cycle terahertz radiation, extending concepts of microwave electron pulse compression and streaking to terahertz frequencies. Optical-field control of electron pulses provides synchronism to laser pulses and offers a temporal resolution that is ultimately limited by the rise-time of the optical fields applied. We used few-cycle waveforms carried at 0.3 terahertz to compress electron pulses by a factor of 12 with a timing stability of <4 femtoseconds (root mean square) and measure them by means of field-induced beam deflection (streaking). Scaling the concept toward multiterahertz control fields holds promise for approaching the electronic time scale in time-resolved electron diffraction and microscopy.

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...