  Holography relies on the interference between a known reference and a signal
of interest to reconstruct both the amplitude and phase of that signal.
Commonly performed with photons and electrons, it finds numerous applications
in imaging, cryptography and arts. With electrons, the extension of holography
to the ultrafast time domain remains a challenge, although it would yield the
highest possible combined spatio-temporal resolution. Here, we show that
holograms of local electromagnetic fields can be obtained with combined
attosecond/nanometer resolution in an ultrafast transmission electron
microscope (UEM). Unlike conventional holography, where the signal and the
reference are spatially separated and then recombined to interfere, in our
method we use electromagnetic fields to split an electron wave function in a
quantum coherent superposition of different energy states. In the image plane,
spatial modulation of the electron-energy distribution reflects the phase
relation between reference and signal fields, which we map via energy-filtered
UEM. Beyond imaging applications, this approach allows implementing
optically-controlled and spatially-resolved quantum measurements in parallel,
providing an efficient and versatile tool for the exploration of electron
quantum optics.
