Electronic quantum trajectories sculpted by lightwaves

Lightwave electronics has revolutionized our way to control materials. The key idea is to utilize the carrier field of intense light as an alternating voltage to accelerate electrons faster than an optical cycle. On subcycle time scales, electrons can move ballistically without scattering, even in solids, unleashing a fascinating coherent quantum world full of promise for future quantum technologies. We will discuss prominent examples of lightwave-driven dynamics in quantum materials, ranging from Bloch oscillations via topologically non-trivial electron trajectories to active band-structure engineering by light. Innovative lightwave-driven microscopes can directly videotape single molecules and atomic defects and observe the subcycle quantum flow of electrons. Our results offer a radically new way of watching and controlling the anatomy of elementary dynamics in physics, chemistry and biology.