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 demonstrate a hybrid architecture consisting of a quantum dot circuit coupled to a single mode of the electromagnetic field. We use single wall carbon nanotube based circuits inserted in superconducting microwave cavities. By probing the nanotube-dot using a dispersive read-out in the Coulomb blockade and the Kondo regime, we determine an electron-photon coupling strength which should enable circuit QED experiments with more complex quantum dot circuits.PACS numbers: 73.63.Fg An atom coupled to a harmonic oscillator is one of the most illuminating paradigms for quantum measurements and amplification [1]. Recently, the joint development of artificial two-level systems and high finesse microwave resonators in superconducting circuits has brought the realization of this model on-chip [2,3]. This "circuit Quantum Electro-Dynamics" architecture allows, at least in principle, to combine circuits with an arbitrary complexity. In this context, quantum dots can also be used as artificial atoms [4,5]. Importantly, these systems often exhibit many-body features if coupled strongly to Fermi seas, as epitomized by the Kondo effect. Combining such quantum dots with microwave cavities would therefore enable the study of a new type of coupled fermionicphotonic systems.Cavity quantum electrodynamics [6] and its electronic counterpart circuit quantum electrodynamics[1] address the interaction of light and matter in their most simple form i.e. down to a single photon and a single atom (real or artificial). In the field of strongly correlated electronic systems, the Anderson model follows the same purified spirit [7]. It describes a single electronic level with onsite Coulomb repulsion coupled to a Fermi sea. In spite of its apparent simplicity, this model allows to capture non-trivial many body features of electronic transport in nanoscale circuits. It contains a wide spectrum of physical phenomena ranging from resonant tunnelling and Coulomb blockade to the Kondo effect. Thanks to progress in nanofabrication techniques, the Anderson model has been emulated in quantum dots made out of two dimensional electron gas[8], C60 molecules [9] or carbone nanotubes [10]. Here, we mix the two above situations. We couple a quantum dot in the Coulomb blockade or in the Kondo regime to a single mode of the electromagnetic field and take a step further towards circuit QED experiments with quantum dots. * To whom correspondence should be addressed: kontos@lpa.ens. fr FIG. 1: a. Schematics of the quantum dot embedded in the microwave cavity. The transmitted microwave field has different amplitude and phase from the input field as a result of its interaction with the quantum dot inside the cavity. The quantum dot is connected to "wires" and capacitively coupled to a gate electrode in the conventional 3-terminal transport geometry. b. Scanning electron microscope (SEM) picture in false colors of the coplanar waveguide resonator. Both the typical coupling capacitance geometry of one port of the resonator and the 3-terminals geometry are visib...

Many-body correlations and macroscopic quantum behaviors are fascinating condensed matter problems. A powerful test-bed for the many-body concepts and methods is the Kondo model 1,2 which entails the coupling of a quantum impurity to a continuum of states. It is central in highly correlated systems 3-5 and can be explored with tunable nanostructures 6-9 . Although Kondo physics is usually associated with the hybridization of itinerant electrons with microscopic magnetic moments 10 , theory predicts that it can arise whenever degenerate quantum states are coupled to a continuum 4,11-14 . Here we demonstrate the previously elusive 'charge' Kondo effect in a hybrid metal-semiconductor implementation of a singleelectron transistor, with a quantum pseudospin-1 2 constituted by two degenerate macroscopic charge states of a metallic island 11,[15][16][17][18][19][20] . In contrast to other Kondo nanostructures, each conduction channel connecting the island to an electrode constitutes a distinct and fully tunable Kondo channel 11 , thereby providing an unprecedented access to the two-channel Kondo effect and a clear path to multi-channel Kondo physics 1,4,21,22 . Using a weakly coupled probe, we reveal the renormalization flow, as temperature is reduced, of two Kondo channels competing to screen the charge pseudospin. This provides a direct view of how the predicted quantum phase transition develops across the symmetric quantum critical point 4,21 . Detuning the pseudospin away from degeneracy, we demonstrate, on a fully characterized device, quantitative agreement with the predictions for the finite-temperature crossover from quantum criticality 17 .In previous experimental investigations, the Kondo quantum impurity was of microscopic nature and mostly associated with spin 6,7,9,23-25 , orbital 8,26 , or possibly structural degrees of freedom 4,27 . In the 'charge' Kondo effect 11,16,17 , it is a pseudospin-1 2 constituted of two degenerate states of a macroscopic quantum variable, the electrical charge of a metallic island comprising several billions of electrons. The role of the electrons' spin (↑↓) in the original spin Kondo problem 10 is played by the electrons' location, in the island (↑) or elsewhere (↓). Accordingly, the charge pseudospin flips when electrons are transferred in and out of the island. The Kondo channels, each coupling the Kondo impurity (pseudo)spin with a distinct electron continuum, directly equate with the different electrical conduction channels connected to the island (distinguishing between those associated with different values of the real electron spin). In contrast, * e-mail: frederic.pierre@lpn.cnrs.fr Hybrid metal-semiconductor singleelectron transistor. a, Colorized picture of the sample (schematic in inset) constituted of a central metallic island (bright) connected to large electrodes (white circles) through the quantum point contacts QPC1,2 formed in a buried 2D electron gas (darker gray). The lateral continuous gates and QPCp are used, respectively, to characterize the 'intrinsic...

The edge channels of the quantum Hall effect provide one dimensional chiral and ballistic wires along which electrons can be guided in an optics-like setup. Electronic propagation can then be analyzed using concepts and tools derived from optics. After a brief review of electron optics experiments performed using stationary current sources which continuously emit electrons in the conductor, this paper focuses on triggered sources, which can generate on-demand a single particle state. It first outlines the electron optics formalism and its analogies and differences with photon optics and then turns to the presentation of single electron emitters and their characterization through the measurements of the average electrical current and its correlations. This is followed by a discussion of electron quantum optics experiments in the Hanbury-Brown and Twiss geometry where two-particle interferences occur. Finally, Coulomb interactions effects and their influence on single electron states are considered.

In analogy with quantum optics, short time correlations of the current fluctuations are measured and used to assess the quality of the single particle emission of a recently introduced on-demand electron source. We observe, for the first time in the context of electronics, the fundamental noise limit associated with the quantum fluctuations of the emission time of single particles, or quantum jittering. In optimum operating conditions of the source, the noise reduces to the quantum jitter limit, which demonstrates single particle emission. Combined with the coherent manipulations of single electrons in a quantum conductor, this electron quantum optics experiment opens the way to explore new problems including quantum statistics and interactions at the single electron level.

We have realized a quantum optics like Hanbury Brown and Twiss (HBT) experiment by partitioning, on an electronic beam-splitter, single elementary electronic excitations produced one by one by an on-demand emitter. We show that the measurement of the output currents correlations in the HBT geometry provides a direct counting, at the single charge level, of the elementary excitations (electron/hole pairs) generated by the emitter at each cycle. We observe the antibunching of low energy excitations emitted by the source with thermal excitations of the Fermi sea already present in the input leads of the splitter, which suppresses their contribution to the partition noise. This effect is used to probe the energy distribution of the emitted wave-packets.The development of quantum electronics based on the coherent manipulation of single to few quasi-particles in a ballistic quantum conductor has raised a strong interest in the recent years [1][2][3][4][5][6][7]. On the theoretical side, many proposals have suggested to generate and manipulate single electronic excitations in optics like setups [2][3][4] and to use them in Fermion based quantum information processing [5]. On the experimental side, triggered electron sources that supply single electron states on-demand have been demonstrated [6,7] but there has been no report so far of their implementation in an electron quantum optics experiment (i.e electron optics at the single charge level). Actually, the very principle of electron quantum optics is still under question as singling out a single elementary excitation remains a complex issue [8] in solid state where the Fermi sea builds up from many interacting electrons.In this work, we have realized the partitioning of single electron/hole excitations emitted one by one by the on demand electron source we recently developed [6] using an electronic beam splitter in the Hanbury Brown and Twiss geometry [9]. From low frequency current correlations measurements, we count the number of elementary excitations produced by the source at the single charge level. We also demonstrate that the random partitioning of low energy excitations produced by the source is suppressed by their antibunching with thermal excitations of the Fermi sea. This quantum effect provides an efficient tool to probe the energy distribution of the individual quantum states produced by the source. By tuning the emission parameters we show that the energy distribution can be shaped in a controlled manner. Finally, this work defines the proper conditions for the manipulation of a single elementary excitation in the presence of a thermal bath.Electron quantum optics, like its photonic counterpart, relies on the manipulation of single particle states supplied on-demand and characterized by the measurements of current-current correlations. The study of currentcurrent correlations in quantum conductors has been widely used to probe the statistics of particles emitted by a source. The most common source is the DC biased contact which produces a stationary cur...

We propose a quantum tomography protocol to measure single electron coherence in quantum Hall edge channels and therefore access for the first time the wave function of single electron excitations propagating in ballistic quantum conductors. Its implementation would open the way to quantitative studies of single electron decoherence and would provide a quantitative tool for analyzing single to few electron sources. We show how this protocol could be implemented using ultrahigh sensitivity noise measurement schemes.

The controlled and accurate emission of coherent electronic wave packets is of prime importance for future applications of nano-scale electronics. Here we present a theoretical and experimental analysis of the finite-frequency noise spectrum of a periodically driven single electron emitter. The electron source consists of a mesoscopic capacitor that emits single electrons and holes into a chiral edge state of a quantum Hall sample. We compare experimental results with two complementary theoretical descriptions: On one hand, the Floquet scattering theory which leads to accurate numerical results for the noise spectrum under all relevant operating conditions. On the other hand, a semi-classical model which enables us to develop an analytic description of the main sources of noise when the emitter is operated under optimal conditions. We find excellent agreement between experiment and theory. Importantly, the noise spectrum provides us with an accurate description and characterization of the mesoscopic capacitor when operated as a periodic single electron emitter. PACS numbers: 73.23.-b, 73.63.-b, 72.70.+m arXiv:1111.3136v1 [cond-mat.mes-hall]