A. Cavanna

Separation of neutral and charge modes in one-dimensional chiral edge channels

Coulomb interactions have a major role in one-dimensional electronic transport. They modify the nature of the elementary excitations from Landau quasiparticles in higher dimensions to collective excitations in one dimension. Here we report the direct observation of the collective neutral and charge modes of the two chiral co-propagating edge channels of opposite spins of the quantum Hall effect at filling factor 2. Generating a charge density wave at frequency f in the outer channel, we measure the current induced by inter-channel Coulomb interaction in the inner channel after a 3-μm propagation length. Varying the driving frequency from 0.7 to 11 GHz, we observe damped oscillations in the induced current that result from the phase shift between the fast charge and slow neutral eigenmodes. We measure the dispersion relation and dissipation of the neutral mode from which we deduce quantitative information on the interaction range and parameters.

Hong-Ou-Mandel experiment for temporal investigation of single-electron fractionalization

Coulomb interaction has a striking effect on electronic propagation in one-dimensional conductors. The interaction of an elementary excitation with neighbouring conductors favours the emergence of collective modes, which eventually leads to the destruction of the Landau quasiparticle. In this process, an injected electron tends to fractionalize into separated pulses carrying a fraction of the electron charge. Here we use two-particle interferences in the electronic analogue of the Hong-Ou-Mandel experiment in a quantum Hall conductor at filling factor 2 to probe the fate of a single electron emitted in the outer edge channel and interacting with the inner one. By studying both channels, we analyse the propagation of the single electron and the generation of interaction-induced collective excitations in the inner channel. These complementary pieces of information reveal the fractionalization process in the time domain and establish its relevance for the destruction of the quasiparticle, which degrades into the collective modes.

Tomonaga–Luttinger physics in electronic quantum circuits

In one-dimensional conductors, interactions result in correlated electronic systems. At low energy, a hallmark signature of the so-called Tomonaga–Luttinger liquids is the universal conductance curve predicted in presence of an impurity. A seemingly different topic is the quantum laws of electricity, when distinct quantum conductors are assembled in a circuit. In particular, the conductances are suppressed at low energy, a phenomenon called dynamical Coulomb blockade. Here we investigate the conductance of mesoscopic circuits constituted by a short single-channel quantum conductor in series with a resistance, and demonstrate a proposed link to Tomonaga–Luttinger physics. We reformulate and establish experimentally a recently derived phenomenological expression for the conductance using a wide range of circuits, including carbon nanotube data obtained elsewhere. By confronting both conductance data and phenomenological expression with the universal Tomonaga–Luttinger conductance curve, we demonstrate experimentally the predicted mapping between dynamical Coulomb blockade and the transport across a Tomonaga–Luttinger liquid with an impurity.

An On-Demand Coherent Single Electron Source

We report on the electron analog of the single-photon gun. On-demand single-electron injection in a quantum conductor was obtained using a quantum dot connected to the conductor via a tunnel barrier. Electron emission was triggered by the application of a potential step that compensated for the dot-charging energy. Depending on the barrier transparency, the quantum emission time ranged from 0.1 to 10 nanoseconds. The single-electron source should prove useful for the use of quantum bits in ballistic conductors. Additionally, periodic sequences of single-electron emission and absorption generate a quantized alternating current.

Violation of Kirchhoff's Laws for a Coherent RC Circuit

What is the complex impedance of a fully coherent quantum resistance-capacitance (RC) circuit at gigahertz frequencies in which a resistor and a capacitor are connected in series? While Kirchhoffs laws predict addition of capacitor and resistor impedances, we report on observation of a different behavior. The resistance, here associated with charge relaxation, differs from the usual transport resistance given by the Landauer formula. In particular, for a single-mode conductor, the charge-relaxation resistance is half the resistance quantum, regardless of the transmission of the mode. The new mesoscopic effect reported here is relevant for the dynamical regime of all quantum devices.

Coherence and Indistinguishability of Single Electrons Emitted by Independent Sources.

Interfering Single Electrons Quantum information processing requires the generation of indistinguishable and coherent particles. While these have been demonstrated for photons, carrying it over for electrons and the possibility of quantum electronic implementations has been challenging. Using two independent single-electron sources patterned into a two-dimensional electron gas, Bocquillon et al. (p. 1054, published online 24 January; see the Perspective by Schönenberger) performed single-electron interference experiments. The results demonstrate that the generated electrons can possess the desired properties for potential quantum applications. The interference of single electrons emitted from independent sources is demonstrated. [Also see Perspective by Schönenberger] The on-demand emission of coherent and indistinguishable electrons by independent synchronized sources is a challenging task of quantum electronics, in particular regarding its application for quantum information processing. Using two independent on-demand electron sources, we triggered the emission of two single-electron wave packets at different inputs of an electronic beam splitter. Whereas classical particles would be randomly partitioned by the splitter, we observed two-particle interference resulting from quantum exchange. Both electrons, emitted in indistinguishable wave packets with synchronized arrival time on the splitter, exited in different outputs as recorded by the low-frequency current noise. The demonstration of two-electron interference provides the possibility of manipulating coherent and indistinguishable single-electron wave packets in quantum conductors.

Quantum Limit of Heat Flow Across a Single Electronic Channel

Quantum Heating Mesoscopic wires exhibit peculiar properties at low temperatures. Their electric conductance can show plateaus at evenly spaced values, which reflects the sequential opening of “quantum transport channels,” each of which can only carry a finite amount of charge or heat. Whereas the step size for the electric conductance depends on the type of the particle carrying the charge, for heat conduction this “quantum” is universal. Jezouin et al. (p. 601, published online 3 October; see the Perspective by Sothmann and Flindt) measured the quantum of heat conduction through a single electronic channel by comparing the amount of heat needed to heat a small metal plate to a constant temperature, while varying the number of electronic channels through which the heat was dissipated from the plate. Encouragingly, the measurement was in agreement with the theoretical prediction. The unit of heat carried by electrons is measured using noise thermometry and found to be consistent with predictions. [Also see Perspective by Sothmann and Flindt] Quantum physics predicts that there is a fundamental maximum heat conductance across a single transport channel and that this thermal conductance quantum, GQ, 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 GQ 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.

Hot electron cooling by acoustic phonons in graphene.

We have investigated the energy loss of hot electrons in metallic graphene by means of GHz noise thermometry at liquid helium temperature. We observe the electronic temperature T ∝ V at low bias in agreement with the heat diffusion to the leads described by the Wiedemann-Franz law. We report on T ∝ √V behavior at high bias, which corresponds to a T(4) dependence of the cooling power. This is the signature of a 2D acoustic phonon cooling mechanism. From a heat equation analysis of the two regimes we extract accurate values of the electron-acoustic phonon coupling constant Σ in monolayer graphene. Our measurements point to an important effect of lattice disorder in the reduction of Σ, not yet considered by theory. Moreover, our study provides a strong and firm support to the rising field of graphene bolometric detectors.

Direct measurement of the coherence length of edge states in the integer quantum Hall regime.

We have determined the finite temperature coherence length of edge states in the integer quantum Hall effect regime. This was realized by measuring the visibility of electronic Mach-Zehnder interferometers of different sizes, at filling factor 2. The visibility shows an exponential decay with the temperature. The characteristic temperature scale is found inversely proportional to the length of the interferometer arm, allowing one to define a coherence length l_(phi). The variations of l_(phi) with magnetic field are the same for all samples, with a maximum located at the upper end of the quantum Hall plateau. Our results provide the first accurate determination of l_(phi) in the quantum Hall regime.

Non-equilibrium edge-channel spectroscopy in the integer quantum Hall regime

Gapless edge-state excitations known as one-dimensional chiral fermions explain many experimental observations of the behaviour of integer quantum Hall systems. But prevailing theory suggests the emergence of extra edge states as well. A new spectroscopic technique for probing the flow of energy in the edge channels of a quantum Hall device finds no loss of energy to such extra states.