Quantum Hall edge channels at integer filling factor provide a unique test-bench to understand decoherence and relaxation of single electronic excitations in a ballistic quantum conductor. In this Letter, we obtain a full visualization of the decoherence scenario of energy (Landau) and time (Levitov) resolved single electron excitations at filling factor ν = 2. We show that the Landau excitation exhibits a fast relaxation followed by spin-charge separation whereas the Levitov excitation only experiences spin-charge separation. We finally suggest to use Hong-Ou-Mandel type experiments to probe specific signatures of these different scenarios.PACS numbers: 71.10.Pm, 73.43.Lp The recent demonstration of on-demand single electron sources able to inject single electronic excitations into quantum Hall edge channels 1-3 or 2DEG 4,5 has opened a new era of quantum coherent electronics. By combining these sources to electronic beam splitters, experiments analogous to the celebrated Hanbury-Brown and Twiss and Hong-Ou-Mandel 6 experiments have been demonstrated at the single electron level 7,8 thus opening the way to electron quantum optics 9,10 . However, this emerging field goes beyond a simple analogy with photon quantum optics: first of all, the Fermi statistics of electrons differs from the Bose statistics of photons and leads to the Fermi sea, a state with no analogue in photon quantum optics. Moreover, electrically charged electrons experience Coulomb interactions which, despite screening, are expected to induce strong decoherence effects as demonstrated by Mach-Zehnder interferometry experiments [11][12][13][14][15] . Moreover, an in-depth study of the relaxation of a non-equilibrium electronic distribution at filling factor ν = 2 has shown that a description of the quantum Hall edge channels in terms of Landau quasiparticle excitations is not valid 16,17 .Although the above results on single electron relaxation and decoherence have been obtained by considering stationary sources and time averaged quantities such as the electron distribution function, the recent demonstration of the electronic Hong-Ou-Mandel (HOM) experiment 8 calls for a time resolved approach to single electron coherence taking into account the finite duration of the electronic excitation. The aim of this Letter is precisely to discuss the decoherence scenario of two single electron excitations emitted by state of the art sources. First, the Landau quasi-particles correspond to a Lorentzian wave packet in energy emitted by a properly operated quantum dot 1 . Secondly, the Levitov quasi-particles or Levitons 4 are the minimal single electron state obtained by applying a Lorentzian time-dependent potential with quantized flux 18 . We show that comparing the real time aspects of their decoherence brings a better understanding of the underlying mechanisms of electronic decoherence whose specific features could be experimentally tested in HOM experiments.Recently, finite frequency admittance measurements have demonstrated the existence of collecti...

Interedge channel interactions in the quantum Hall regime at filling factor = 2 are analyzed within a plasmon scattering formalism. We derive analytical expressions for energy redistribution among edge channels and for high-frequency noise, which are shown to fully characterize the low energy plasmon scattering. In the strong-interaction limit, the predictions for energy redistribution are compared with recent experimental data and found to reproduce most of the observed features. Quantitative agreement can be achieved by assuming 25% of the injected energy is lost toward other degrees of freedom, possibly the additional gapless excitations predicted for smooth edge potentials.Electronic transport along the chiral edges of a twodimensional electron gas ͑2DEG͒ in the quantum Hall ͑QH͒ regime can now be studied using a single electron source, 1 thus opening the way to fundamental electron optics experiments such as single electron Mach-Zehnder interferometry ͑MZI͒ ͑Ref. 2͒ or Hong-Ou-Mandel experiments. 3 However, contrary to photons, electrons strongly interact through the Coulomb interaction. This leads to relaxation and decoherence phenomena and thereby questions the whole concept of electron quantum optics. The = 2 filling factor is particularly appropriate to address this issue since the electromagnetic environment of one edge channel ͑EC͒ mainly consists of the other EC. In this respect, it is an ideal test bed to investigate interaction effects in the QH regime.Coulomb interactions lead to plasmon scattering which in turn basically determines the linear transport properties of one dimensional systems: finite frequency admittances 4 and thermal conductivity. 5,6 Recently it was pointed out as a key ingredient for understanding the interference contrast of Mach-Zehnder interferometers at =2 ͑Ref. 7͒ and single electron relaxation along ECs. 8 However, despite its fundamental role in the QH regime low energy physics, plasmon scattering has only been indirectly probed through electron quantum interferences ͑MZI͒. 9-12 Recent progresses in the measurements of high-frequency admittance, 13,14 noise 15 and electron distribution function 16 in these systems open new complementary ways to probe the dynamics of QH ECs.In this Rapid Communication, we discuss how the study of energy relaxation and high-frequency noise in a = 2 system will permit us to reach a much deeper understanding of the low energy physics of the QH regime. By studying plasmon scattering within the simplest model for = 2 EC, we derive explicit expressions for frequency admittances in the six-terminal geometry depicted in Fig. 1 and energy exchanges between the two ECs. Comparison with recently obtained experimental data on electron relaxation of the =2 system 17 shows that this model captures most of the physics of this system. However, we observe a small but significant discrepancy between raw data and predictions which demonstrates that part of the energy has leaked out, most likely toward the predicted internal EC modes. 19,20 This constitutes th...