Ballistic electrons splashing down in a Fermi sea of a 1-dimenssional quantum Hall liquid*

The one-dimensional, chiral and dissipationless edge channels of the quantum Hall effect are good canditates to form the electrical analogue of optical fibers, which alllows to coherently manipulate the propagation of single electronic wave packets. However Coulomb interactions between neighboring edge channels can lead to energy relaxation. We explore this phenomenon by measuring the energy distribution function of quasiparticles emitted at well-defined energy in an edge channel at filling factor ν = 2. Our setup relies on a pair of electrostatically defined quantum dots, used as energy-resolved emitter and detector, tunnel coupled to an edge channel. We show that, on sub-micron lengths, quasiparticles undergo a strong relaxation with a survival probability dropping exponentially with their energy. Remarkably, this relaxation preserves the position and width of the quasiparticle peak in the energy distribution function. Furthermore, at intermediate lengths, we observe a marked revival of the peak at high injection energy. Our findings are qualitatively compatible with the conventionally considered theories, however new ingredients such as dissipation seem crucial in order to provide a more quantitative comparison.