  The basic properties of atoms, molecules and solids are governed by electron
dynamics which take place on extremely short time scales. To measure and
control these dynamics therefore requires ultrafast sources of radiation
combined with efficient detection techniques. The generation of extreme
ultraviolet (XUV) attosecond (1 as = 10-18 s) pulses has, for the first time,
made direct measurements of electron dynamics possible. Nevertheless, while
various applications of attosecond pulses have been demonstrated
experimentally, no one has yet captured or controlled the full three
dimensional motion of an electron on an attosecond time scale. Here we
demonstrate an attosecond quantum stroboscope capable of guiding and imaging
electron motion on a sub-femtosecond (1 fs = 10-15 s) time scale. It is based
on a sequence of identical attosecond pulses which are synchronized with a
guiding laser field. The pulse to pulse separation in the train is tailored to
exactly match an optical cycle of the laser field and the electron momentum
distributions are detected with a velocity map imaging spectrometer (VMIS).
This technique has enabled us to guide ionized electrons back to their parent
ion and image the scattering event. We envision that coherent electron
scattering from atoms, molecules and surfaces captured by the attosecond
quantum stroboscope will complement more traditional scattering techniques
since it provides high temporal as well as spatial resolution.
