Consequences of interactions in quantum Hall edge channels

The topic of electron quantum optics has recently assumed a prominent role in the condensed matter agenda. It aims at generating, manipulating and detecting individual electronic wave-packets ballistically propagating in mesoscopic devices to realize quantum-optical like experiments and set-ups in solid state devices. One of the main open problems in this field is the real time detection of the signal, which is a challenge for nowadays electronics. For this reason, techniques based on finite frequency current noise have been developed in order to reconstruct the time behavior of the signals. In this direction, a deep knowledge of quantum noise is needed in order to properly understand and control the time evolution of wave-packets. Moreover, one of the main differences between conventional quantum optics and electron quantum optics is represented by the fact that electrons are charged interacting particles. This leads to many-body effects which strongly affect the dynamics of excitations and play a major role in various experimental situations. The main purpose of this Thesis is to understand what are the consequences of unavoidable electronic interactions in edge channels of the quantum Hall effect, both in the integer and fractional regimes, on current-current fluctuations (i.e. noise). In particular, we have investigated: - the Hong-Ou-Mandel interferometry in a quantum Hall system at filling factor two, namely the physics of colliding identical excitations. Here, we have shown that the injected electronic wave-packets fractionalize before partitioning at a quantum point contact due to interactions. In addition, we have proposed a measurement protocol to determine the strength of interactions; - the peculiar quantum properties of the microwave radiation emitted by a quantum Hall device at filling factor two in presence of interactions. We have connected the squeezing of the emitted radiation to the current fluctuations comparing two different periodic drives. We have observed that a periodic train of Lorentzian pulses is characterized by a robust squeezing effect even in presence of interaction; - the noise associated to the current flowing between two different fractional quantum Hall edge states, with filling factors belonging to the Laughlin sequence, coupled through a quantum point contact and connected to two reservoirs placed at different temperatures. This noise contribution, known in literature as delta-T noise, is currently subject of an intense research from both the theoretical and the experimental point of view.