Single-electron dynamics in topologically protected systems

Electron quantum optics is a fast growing research field which aims at preparing, controlling and coherently manipulating single- to few-electrons states in mesoscopic condensed matter systems, in the same way as single photons can be manipulated in conventional quantum optics. Recently developed coherent single-electron sources are used to generate few-electron excitations in ballistic conductors, where their propagation is not affected by backscattering and phase coherence is preserved. Among several interesting problems related to electron quantum optics, an important question is whether and how interaction effects can influence the evolution of single-electron excitations generated by coherent sources. This will be the main topic of this thesis, where we investigate the properties of excitations created by applying a voltage pulse to a quantum conductor. The thesis can be conceptually divided into two main blocks, depending on which kind of interactions are taken into account. At first we consider a couple of conduction channels coupled by repulsive electron-electron interactions, focusing on two scenarios. Initially, co-propagating edge channels in the integer quantum Hall effect are considered, followed by counterpropagating channels emerging at the edge of a quantum spin Hall insulators. In both systems, electronic interactions induce a fractionalization process causing the initially generated excitations to split into smaller ones, carrying only a fraction of the injected charge. These fractionalized excitations are carefully analyzed both in the time domain as well as in energy and momentum space, which allows to access their particle-hole content. The analysis is based on an analytic approach relying on Luttinger liquid theory and bosonization techniques and applies to any voltage drive. Moreover, specializing to the relevant case of excitations created by quantized Lorentzian voltage pulses, known as Levitons, we show that the noise generated when they are partitioned at a scatterer is minimal, regardless of interactions. Further on, a completely different kind of interaction is addressed, namely superconducting correlations. In particular, we investigate the transport properties of a superconducting tunnel junction under the effect of an arbitrary periodic drive, showing that Levitons do minimize the low frequency noise in this kind of device too.