Heat transport has large potentialities to unveil new physics in mesoscopic systems. A striking illustration is the integer quantum Hall regime 1 , where the robustness of Hall currents limits information accessible from charge transport 2 . Consequently, the gapless edge excitations are incompletely understood. The effective edge states theory describes them as prototypal one-dimensional chiral fermions 3,4 -a simple picture that explains a large body of observations 5 and calls for quantum information experiments with quantum point contacts in the role of beam splitters 6,7,8,9,10,11 . However, it is in ostensible disagreement with the prevailing theoretical framework that predicts, in most situations 12 , additional gapless edge modes 13 . Here, we present a setup which gives access to the energy distribution, and consequently to the energy current, in an edge channel brought out-of-equilibrium. This provides a stringent test of whether the additional states capture part of the injected energy. Our results show it is not the case and thereby demonstrate regarding energy transport, the quantum optics analogy of quantum point contacts and beam splitters. Beyond the quantum Hall regime, this novel spectroscopy technique opens a new window for heat transport and out-of-equilibrium experiments.The integer quantum Hall effect, discovered nearly thirty years ago 1 , has recently experienced a strong revival driven by milestone experiments toward quantum information with edge states 8,9,14 .Beyond Hall currents, new phenomena have emerged that were unexpected within the free one-dimensional chiral fermions (1DCF) model.The on-going debate triggered by electronic Mach-Zehnder interferometers experiments 8,15,16,17 vividly illustrates the gaps in our understanding. Coulomb interaction is seen as the key ingredient. In addition to its most striking repercussion, the fractional quantum Hall effect 18 , the edge reconstruction (ER) turns out to have deep implications on edge excitations. This phenomenon results from the competition between Coulomb interaction that tends to spread the electronic fluid, and the confinement potential: as the latter gets smoother, the non-interacting edge becomes unstable 19 . Theory predicts new branches of gapless electronic excitations in reconstructed edges 13,20 , which breaks the mapping of an edge channel (EC) onto 1DCF and, possibly, the promising quantum optics analogy. For most edges realized in semi-conductor heterojunctions (except by cleaved edge overgrowth 21 ), ER results in wide compressible ECs separated by narrow incompressible strips 12 and the new excited states are overall neutral internal charge oscillations across the ECs width 13 .In practice, the predicted additional neutral modes areExperimental implementation of nonequilibrium edge channel spectroscopy. a, Schematic description of the energy distributions fD,S(E) spectroscopy with a single active electronic level of tunable energy E lev (VG) in the quantum dot (QD). b, The current IQD (∂IQD/∂VG) is proportional to...

We investigate the energy exchanges along an electronic quantum channel realized in the integer quantum Hall regime at filling factor νL = 2. One of the two edge channels is driven out-ofequilibrium and the resulting electronic energy distribution is measured in the outer channel, after several propagation lengths 0.8 µm≤ L ≤ 30 µm. Whereas there are no discernable energy transfers toward thermalized states, we find efficient energy redistribution between the two channels without particle exchanges. At long distances L ≥ 10 µm, the measured energy distribution is a hot Fermi function whose temperature is lower than expected for two interacting channels, which suggests the contribution of extra degrees of freedom. The observed short energy relaxation length challenges the usual description of quantum Hall excitations as quasiparticles localized in one edge channel.PACS numbers: 73.43. Fj, 72.15.Lh, 73.23.Ad, 73.43.Lp The basic manifestation of the quantum Hall effect is a quantized Hall resistance R H = h/e 2 ν L , accompanied by a vanishing longitudinal resistance. In this regime, quantization of the two-dimensional cyclotron motion opens a large gap separating Landau levels in the bulk of the sample from the Fermi energy. The only available low energy excitations propagate along the edges, where the Landau levels cross the Fermi energy. The effective edge state theory suggests these excitations are prototypal one-dimensional chiral fermions (1DCF) [1], each of the ν L edge channels (EC) being identified with a onedimensional conductor. Because back-scattering is forbidden by chirality, ECs are considered to be ideal ballistic quantum channels. Their similitude with light beams has inspired electronic analogues of quantum optics experiments [2-5] and proposals for quantum information applications [6]. However, the nature and decoherence of edge excitations are poorly understood, as highlighted by unexpected results obtained with electronic MachZehnder interferometers: an unusual energy dependence of the interference fringes' visibility [2, 7], a non-gaussian noise [8] and a short coherence length [9, 10]. Interactions between ECs and with their environment are seen as the key ingredient to explain these results (see e.g. [11, 12]).In the present experimental work, we investigate the interaction mechanisms taking place along an EC through the energy exchanges they induce. A similar approach was previously used on mesoscopic metal wires [13] and on carbon nanotubes [14]. Here we focus on the filling factor ν L = 2, where two co-propagating ECs are present, and at which the above unexpected results were observed. Our experiment relies on the techniques we recently demonstrated to drive out-of-equilibrium an EC and to measure the resulting energy distribution f (E) of 1DCF quasiparticles [15]. There, we drove out-ofequilibrium only the outer EC, and f (E) was measured in the same EC after a short 0.8 µm propagation distance, for which the energy redistribution is negligible. Here, we drive out-of-equilibrium sel...

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...