Abstract
In this thesis, we use theoretical and computational methods to explore how electrons can be shaped, and how shaped electrons can in turn be used to tailor light-matter interactions for quantum nanophotonic applications. In the first part of this thesis, we show that the bound electrons in three-dimensional Dirac semimetals (3D DSMs) possess extreme nonlinearity at low photon energies, making them prime candidates for realizing extreme shaping of terahertz (THz) light through high-harmonic generation (HHG). We show that 3D DSMs can efficiently convert impinging THz light up to its 31st harmonic with input laser intensities & 105 times lower than required for existing THzHHGplatforms. Additionally, unlike the 2D DSM graphene, there exists a regime of operation where all THz nonlinearities beyond the 3rd order are unexpectedly suppressed due to the additional dimension 3D DSMs possesses over 2D DSMs. This breaks the common notion that 3D DSMs and graphene share a qualitatively similar nonlinear response. Accounting for nonlinear propagation dynamics in a 3D DSM film, we also discover the existence of an optimal film thickness beyond which the output HHG intensity drastically falls as a result of its extreme nonlinearity. This constitutes a propagation-induced dephasing effect which can only be observed with extremely nonlinear bulk materials like 3D DSMs. In the second part of this thesis, we introduce two new concepts for shaping lightmatter interactions with free electrons. First, we introduce two-electron quantum photoninduced near-field electron microscopy (QPINEM) interactions, which involve the injection of an additional electron into conventional single-electron QPINEM setups. We show that two-electron QPINEM interactions allow us to shape both the photon and electron statistics with a level of versatility not possible with a single electron (e.g., creation of large Fock states, post-selecting highly asymmetric electron spectra). This versatility in shaping photons and electrons is enabled by non-Coulombic two-electron effects that arise in the limit where light is described nonclassically. Second, we show that shaped free electrons can be used to tailor light-matter interactions through quantum interference (QI). This is revealed through our general framework which describes QI between multiple quantum processes involving arbitrary numbers and types of quantum systems (e.g., electrons, atoms, photons). We apply this framework to 2 examples of light-matter interactions involving shaped free electron wavefunctions to predict the following unprecedented phenomena: (i) For a free electron scattering off a classical light field, the output electron spectrum sees the complete suppression of the zero-loss peak due to destructive QI; (ii) Spontaneous emission from shaped free electrons and atoms can be made to substantialy affect each other through QI despite having no direct interaction (i.e., no Coulomb interaction) between both systems. These results show that the shape of electrons affect not only their own interaction with light, but they can also affect the interaction between other quantum systems with light.