STRELIM · Structuring free-electron wave functions through interaction with structured light and engineered metamaterials

Controlling free-electron wave functions with light has recently emerged as a powerful approach to gaining unprecedented space-time resolution in imaging and manipulating the nanoworld. However, control over the electron wave function has so far been limited to specific low-dimensional spaces, such as the transverse plane, the temporal profile, or the energy distribution. In contrast, accessing multiple dimensions simultaneously remains a complex challenge, which I intend to tackle through this project. The first goal of my project is to search for exotic structures of quantum free-electron waves in high dimensions, exhibiting topological textures and defects beyond a simple vortex. To this end, I will draw inspiration from optical waves to create structured quantum waves that are free-electron solutions of the Dirac equation. In a second goal, I aim to explore the control of free-electron wave functions based on the interaction with structured light to unveil new capabilities enabled by recent advances in spatial or spatiotemporal light shaping, which can, in turn, produce previously inaccessible electron waves. In a third goal, I will explore the use of photonic metamaterials to control free-electron wave functions, capitalizing on an enlarged set of degrees of freedom in the design of metamaterial and the subsequent control of optical fields, which is expected to translate into an enhanced ability to manipulate electron wave functions in spatial, temporal, or spatiotemporal domains. This study should expand the current boundaries of free-electron science and technology through a multidisciplinary approach, pushing beyond current capabilities to unprecedented limits of spatiotemporal resolution, impacting the design of more compact and versatile electron sources (e.g., a deterministic single-electron emitter), and shedding light on multidimensional information comprising space, time, momentum, and spin degrees of freedom.