Diffraction and microscopy with attosecond electron pulse trains

Attosecond spectroscopy(1-7) can resolve electronic processes directly in time, but a movie-like space-time recording is impeded by the too long wavelength (similar to 100 times larger than atomic distances) or the source-sample entanglement in re-collision techniques(8-11). 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(8-11). 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-angstrom 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.