Quantum physics predicts that there is a fundamental maximum heat conductance across a single transport channel, and that this thermal conductance quantum G Q is universal, independent of the type of particles carrying the heat. Such universality, combined with the relationship between heat and information, signals a general limit on information transfer. We report on the quantitative measurement of the quantum limited heat flow for Fermi particles across a single electronic channel, using noise thermometry. The demonstrated agreement with the predicted G Q establishes experimentally this basic building block of quantum thermal transport. The achieved accuracy of below 10% opens access to many experiments involving the quantum manipulation of heat.The transport of electricity and heat in reduced dimensions and at low temperatures is subject to the laws of quantum physics. The Landauer formulation of this problem [1][2][3] introduces the concept of transport channels: a quantum conductor is described as a particle waveguide, and the channels can be viewed as the quantized transverse modes. Quantum physics sets a fundamental limit to the maximum electrical conduction across a single electronic channel. The electrical conductance quantum G e = e 2 h, where e is the unit charge and h is the Planck constant, was initially revealed in ballistic 1D constrictions [4,5]. However, different values of the maximum electrical conductance are observed for different types of charge carrying particles. In contrast, for heat conduction the equivalent thermal conductance quantumT (which sets the maximum thermal conduction across a single transport channel, k B being the Boltzmann constant, T the temperature) is predicted to be independent of the heat carrier statistics, from bosons to fermions including the intermediate 'anyons' [6][7][8][9][10][11][12][13][14][15][16]. In electronic channels, which carry both an electrical and thermal current, the pre-2 )T between G Q and G e verifies and extends the Wiedemann-Franz relation down to a single channel [8,9]. In general, the universality of G Q , together with the deep relationship between heat, entropy and information [17], points to a quantum limit on the flow of information through any individual channel [6,15]. The thermal conductance quantum has been measured for bosons, in systems with as few as 16 phonon channels [18,19], and probed at the single photon channel level [20,21]. For fermions, heat conduction was shown to be proportional to the number of ballistic electrical channels [22,23]. In [22] the data were found compatible, within an order of magnitude estimate, to the predicted thermal conductance quantum, whereas [23] demonstrated more clearly the quantization of thermal transport, but G Q was not accessible by construction of the experiment.We have measured the quantum limited heat flow across a single electronic channel using the conceptually simple approach depicted in Fig. 1A. A micron-sized metal plate is electrically connected by an adjustable number n of ballist...

We present an original statistical method to measure the visibility of interferences in an electronic Mach-Zehnder interferometer in the presence of low frequency fluctuations. The visibility presents a single side lobe structure shown to result from a gaussian phase averaging whose variance is quadratic with the bias. To reinforce our approach and validate our statistical method, the same experiment is also realized with a stable sample. It exhibits the same visibility behavior as the fluctuating one, indicating the intrinsic character of finite bias phase averaging. In both samples, the dilution of the impinging current reduces the variance of the gaussian distribution. Nowadays quantum conductors can be used to perform experiments usually done in optics, where electron beams replace photon beams. A beamlike electron motion can be obtained in the Integer Quantum Hall Effect (IQHE) regime using a high mobility two dimensional electron gas in a high magnetic field at low temperature. In the IQHE regime, one-dimensional gapless excitation modes form, which correspond to electrons drifting along the edge of the sample. The number of these so-called edge channels corresponds to the number of filled Landau levels in the bulk. The chirality of the excitations yields long collision times between quasi-particles, making edge states very suitable for quantum interferences experiments like the electronic Mach-Zehnder interferometer (MZI) [1,2,3]. Surprisingly, despite some experiments which show that equilibrium length in chiral wires is rather long [4], very little is known about the coherence length or the phase averaging in these "perfect" chiral uni-dimensional wires. In particular, while in the very first interference MZI experiment the interference visibility showed a monotonic decrease with voltage bias, which was attributed to phase noise [1], in a more recent paper, a surprising non-monotonic decrease with a lobe structure was observed [5]. A satisfactory explanation has not yet been found, and the experiment has so far not been reported by other groups to confirm these results.We report here on an original method to measure the visibility of interferences in a MZI, when low frequency phase fluctuations prevent direct observation of the periodic interference pattern obtained by changing the magnetic flux through the MZI. We studied the visibility at finite energy and observed a single side lobe structure, which can be explained by a gaussian phase averaging whose variance is proportional to V 2 , where V is the bias voltage. To reinforce our result and check if low frequency fluctuation may be responsible for that behavior, we realized the same experiment on a stable sample : we also observed a single side lobe structure which can be fitted with our approach of gaussian phase averaging. This proves the validity of the results, which cannot be an artefact due to the low frequency phase fluctuations in the first sample. In both samples, the dilution of the impinging current has an unexpected effect : it decreases ...

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...

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...