Quantum effects have been studied on photon propagation in the context of quantum optics since the second half of the last century. In particular, using single photon emitters, fundamental tests of quantum mechanics were explored by manipulating single to few photons in Hanbury-Brown and Twiss and Hong Ou Mandel experiments. In nanophysics, there is a growing interest to translate these concepts of quantum optics to electrons propagating in nanostructures. Single electron emitters have been realized such that single elementary electronic excitations can now be manipulated in the analog of quantum optics experiments. Electron quantum optics goes beyond the mere reproduction of optical setups using electron beams, as electrons, being interacting fermions, differ strongly from photons. Contrary to optics, understanding the propagation of an elementary excitation requires replacing the single body description by a many body one.
The purpose of this proposal was to explore the emergence of many body physics in quantum conductors using the setups and concepts of electron quantum optics. More specifically, this project aimed at unveiling the birth, life and death scenarii of elementary Landau quasiparticles. Secondly, the project addressed the generation of entangled few electrons quantum coherent states and study how they are affected by interactions. Finally, the project aimed at applying electron quantum optics concepts to a regime where the ground state itself is a strongly correlated state of matter. In such a situation, elementary excitations are no longer electrons but anyons carrying a fractional charge and obeying fractional statistics. Experimental evidence of the fractional statistics of anyons remained elusive for a long time.
At the end of this proposal, several of its objectives have been fulfilled. The decoherence scenario of single electronic excitations has been completely characterized and understood by combining experiments and theory. We have also been able to implement tomography protocols for electronic states bases on two-particle interferometry in collider geometries. In these setups, one can fully extract an elementary description of quantum electrical currents in terms of elementary electron and hole wavefunctions with their emission probabilities. Regarding the characterization of two-electron entanglement, the project investigated theoretically the possibility to measure two-electron coherence and entanglement using the electronic analog of the Fransson interferometer. Finally the most important outcomes of the project are related to electron quantum optics experiments in the fractional quantum effect. In particular, we have been able to demonstrate the fractional statistics of anyons, which are the elementary excitations of fractional quantum Hall fluids, using two-particle interferences in the geometry of a collider.
