Mach Zehnder interferometry and coherent manipulation of the valley in a graphene PN junction

Electron quantum optics, i.e. the realization of the electronic analogue of quantum optics experiments, represents a developing and recent research field, offering interesting perspectives for quantum computing. In this context, one of the main stakes is the achievement of quantum bits using electronic states, as well as the creation of entangled electronic states, which are the building blocks to achieve complex quantum computations. Up to now, the experiments carried out in semi-conducting GaAs/AlGaAs heterostructures exhibited the possibility to encode information in the charge or the spin of an electron, but strong decoherence in these systems implies a great weakness of these quantum states, which survives only below temperatures of 100mK and electrical biases of 40μV. This fragility makes it difficult to achieve entangled states and limits the development of complex quantum computations. In 2005, the discovery of a novel material, graphene, opened new prospects with on one hand the prediction of a larger phase coherence, and on the other hand the existence, in addition to the spin, of a new degree of freedom, named the valley, giving access to new possibilities to encode information. In a first part, this PhD work deals with the coherent manipulation of the valley, which is necessary to achieve a valley quantum bit in graphene. For this aim, we used, in the quantum Hall regime, a graphene pn junction, formed thanks to gates deposited on top of a stack composed of a graphene sheet encapsulated in Boron nitride crystals. In order to obtain an electrostatic control of the valley polarization of incoming electrons, we deposited local gates at the intersections between the pn junction and the graphene physical edge. Associating this electrostatic control to a tuning of the Aharanov-Bohm phase, we can coherently manipulate the valley of an electron over the whole states described by a valley Bloch sphere. In what follows, the coherence of the quantum states is investigated thanks to Mach Zehnder interferometry, by measuring the interferences dependence on the chemical potential of incoming electrons and on the temperature of the system. The quantum states formed are exceptionally steady, they persist up to 1.5K and 1mV, in other words at energies 20 times higher than what was observed in GaAs/AlGaAs.Then, the manuscript describes the study of the coherence length, i.e. the distance on which an electron can propagate while keeping its phase coherence, which has never been measured in the quantum Hall regime in graphene. To that end, the interferences dependence on the temperature was measured in three pn junctions of different lengths. By doing so, two coherence lengths, corresponding to two different regimes of decoherence, were extracted; in the regime occurring at low temperature, a record value of 374μm at 20mK was obtained.Finally, we investigated one of the mechanisms of decoherence in our system: spin waves, propagating in the graphene bulk when it is magnetized. During this project, we have shown the possibility to encode information in the valley and to manipulate coherently this degree of freedom, paving the way towards a new domain: the valleytronics. Furthermore, the coherence of the system is exceptional, enabling to envision the achievement of entangled electronic states by using a double Mach Zehnder interferometer geometry. This opens promising prospects for quantum computing, but also for fundamental purposes, with the possibility to demonstrate, for the first time with fermions, the validity of the Copenhagen interpretation of quantum physics within the EPR paradox framework.