Electron quantum optics at fractional filling factor: minimal excitation states and interferometry

The emerging field of electron quantum optics aims at manipulating electrons one by one in ballistic, coherent conductors. In this way it is possible to reproduce quantum-optical experiments and setups in solid state devices, using fermionic degrees of freedom (electrons in mesoscopic systems) instead of bosonic ones (photons in waveguides and optical cavities). However, the solid state world can be heavily influenced by electron-electron interactions, differently to what happens in the traditional photonic quantum optics. In this thesis, we discuss how electron quantum optics can be extended to the fractional quantum Hall regime, where interactions give rise to exotic quasi-particles carrying a fraction of the electron charge, and whose statistical properties are neither bosonic nor fermionic, but belongs to the more general class of anyons. In particular, we discuss a strategy to excite coherent single-electron excitations in the fractional liquid by means of carefully-engineered voltage pulses applied to the conductor, and show how to detect such a unique quantum state in a fermionic Hanbury-Brown and Twiss experiment. We also analyze collisions of identical excitations in the fractional quantum Hall regime, in the spirit of the celebrated Hong-Ou-Mandel experiment, highlighting analogies and differences with respect to ordinary fermionic systems.