Inelastic Scattering of Transversely Phase-Structured Free Electrons

Abstract

Recent developments in abilities to produce, parse, and measure the electron's wave function within the transmission electron microscope (TEM) and scanning TEM (STEM), have sparked renewed theoretical interest in quantum mechanical treatments of inelastic electron scattering observables and the information they contain. Optical selection rules, originating from the intrinsic spin and linear momentum degrees of the photon, are commonly leveraged in optical-based spectromicroscopies. Although quantum mechanical treatments of inelastic electron scattering have been well understood in core-loss electron energy loss spectroscopy (EELS) for decades, recent demonstrations shaping the electron wave function in the low-loss regime has driven renewed interest in quantum mechanical treatments of the electron probe. Borrowing ideas from the field of quantum optics, the creation and manipulation of transversely structured vortex (or twisted) electron beams has enabled vectorially-resolved electron energy loss and gain measurements of nanoscale and quantum materials. Additionally, the preparation of free electron qubits endowed with quantum information in the form of quantized energy or topological charge, via structured laser pules, spiral phase plates, and holographic masks, has contributed to the recognition of electrons as potential carriers of quantum information. This dissertation explores the quantum electrodynamics of inelastic electron scattering, with particular emphasis placed upon the investigation and development of novel electron scattering observables and the information they encode.