Free electrons have strong potential as tools that allow us to sample and modify quantum optical fields. Thanks to recent advancements in electron microscope technology and the manipulation of free electrons, including the synthesis of femtosecond electron wave packets that are synchronized with femtosecond light pulses, we are now able to control the longitudinal and transverse wave functions of free electrons and their interaction with nanoscale optical excitations. In this presentation, we will offer an overview of the fundamental principles ruling the interactions between free electrons, light, and photonic nanostructures. We will place particular emphasis on exploring the quantum aspects of these interactions, including a variety of intriguing challenges and emerging possibilities. Furthermore, we will discuss potential applications such as noninvasive spectroscopy and microscopy, the potential for the measurement of nonlinear optical responses with nanoscale spatial detail, the manipulation of density matrices related to free electrons and optical modes within small-scale specimens, and optical manipulation of electron beams.
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