  Laser-based preparation, manipulation, and readout of the states of quantum
particles has become a powerful research tool that has enabled the most precise
measurements of time, fundamental constants, and electromagnetic fields. Laser
control of free electrons can improve the detection of electrons' interaction
with material objects, thereby advancing the exploration of matter on the
atomic scale. For example, temporal modulation of electron waves with light has
enabled the study of transient processes with attosecond resolution. In
contrast, laser-based spatial shaping of the electron wave function has not yet
been realized, even though it could be harnessed to probe radiation-sensitive
systems, such as biological macromolecules, at the standard quantum limit and
beyond. Here, we demonstrate laser control of the spatial phase profile of the
electron wave function and apply it to enhance the image contrast in
transmission electron microscopy. We first realize an electron interferometer,
using continuous-wave laser-induced retardation to coherently split the
electron beam, and capture TEM images of the light wave. We then demonstrate
Zernike phase contrast by using the laser beam to shift the phase of the
electron wave scattered by a specimen relative to the unscattered wave.
Laser-based Zernike phase contrast will advance TEM studies of protein
structure, cell organization, and complex materials. The versatile coherent
control of free electrons demonstrated here paves the way towards
quantum-limited detection and new imaging modalities.
