We study free-space electron waves and their interactions with light, both as an intriguing quantum system and as a scientific tool. We use laser beams to shape electron wave functions in space and time, creating electron quantum states with as yet unexplored properties. Such engineered electron waves enable new approaches in electron microscopy and spectroscopy, new radiation sources, and new ways to control quantum systems on the nanoscale.

We also pursue an exploratory project where high-intensity laser light interacts with virtual electrons (and positrons): probing electromagnetic nonlinearity of physical vacuum in an all-optical tabletop experiment.