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...

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...

In apparent contradiction to the laws of thermodynamics, Maxwell's demon is able to cyclically extract work from a system in contact with a thermal bath, exploiting the information about its microstate. The resolution of this paradox required the insight that an intimate relationship exists between information and thermodynamics. Here, we realize a Maxwell demon experiment that tracks the state of each constituent in both the classical and quantum regimes. The demon is a microwave cavity that encodes quantum information about a superconducting qubit and converts information into work by powering up a propagating microwave pulse by stimulated emission. Thanks to the high level of control of superconducting circuits, we directly measure the extracted work and quantify the entropy remaining in the demon's memory. This experiment provides an enlightening illustration of the interplay of thermodynamics with quantum information.quantum thermodynamics | superconducting circuits | quantum information I n 1867, pondering the newly developed thermodynamic laws, Maxwell came to the disturbing conclusion that a "demon" can extract work cyclically from a thermodynamic system beyond the limits set by the second law when acting upon the information it obtains about the system (1). This paradox was resolved a century later when Landauer realized that information processing has an entropic cost and Bennett argued that the demon's memory must take full part in the thermodynamic cycle (2). Recent experiments have realized classical versions of elementary Maxwell demons in various physical systems (3-8). Although quantum versions have long been investigated theoretically (9-13), experimental realizations are in their infancy (7,8), and a full characterization is still missing. Using superconducting circuits, we reveal the inner mechanics of a quantum Maxwell demon that is able to extract work from a quantum system. Importantly, we are able to directly probe the extracted work by measuring the output power emitted by the system through stimulated emission, without inferring it from system trajectories (3-6, 14). We are thus able to demonstrate how the information stored in the demon's memory affects the extracted work. To make the characterization complete, we also measure the entropy and energy of the system and the demon. Superconducting circuits thus reveal themselves as a suitable experimental testbed for the blooming field of quantum thermodynamics of information (15)(16)(17)(18)(19).In the experiment, the system S is a transmon superconducting qubit (20) with energy difference hfS = h × 7.09 GHz between its ground |g and excited |e states. It is embedded in a microwave cavity that resonates at fD = 7.91 GHz and plays the role of the demon's memory D. The dispersive Hamiltonian reads H = hfS |e e|S + hfD d † d − hχd † d |e e|S , where d is the annihilation operator of a photon in the cavity. The last term induces a frequency shift of the cavity by −χ = −33 MHz when the qubit is excited. Reciprocally, the qubit frequency is shif...

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.

The question of which laws govern electricity in mesoscopic circuits is a fundamental matter that also has direct implications for the quantum engineering of nanoelectronic devices. When a quantum-coherent conductor is inserted into a circuit, its transport properties are modified; in particular, its conductance is reduced because of the circuit back-action. This phenomenon, known as environmental Coulomb blockade, results from the granularity of charge transfers across the coherent conductor 1 . Although extensively studied for a tunnel junction in a linear circuit 2-5 , it is only fully understood for arbitrary short coherent conductors in the limit of small circuit impedances and small conductance reduction 6-8 . Here, we investigate experimentally the strong-back-action regime, with a conductance reduction of up to 90%. This is achieved by embedding a single quantum channel of tunable transmission in an adjustable on-chip circuit of impedance comparable to the resistance quantum R K = h/e 2 at microwave frequencies. The experiment reveals significant deviations from calculations performed in the weak back-action framework 6,7 , and is in agreement with recent theoretical results 9,10 . Based on these measurements, we propose a generalized expression for the conductance of an arbitrary quantum channel embedded in a linear circuit.The transport properties of a coherent conductor depend on the surrounding circuit. First, electronic quantum interferences blend the conductor with its vicinity, resulting in a different coherent conductor (see for example ref. 11). Furthermore, the circuit backaction modifies the full counting statistics of charge transfers across coherent conductors 9,10,12 . This mechanism, which is our concern here, results in violations of the classical impedance composition laws even for distinct circuit elements, separated by more than the electronic phase coherence length. The present experimental work investigates the strong circuit back-action on the conductance of an arbitrary electronic quantum channel.The circuit back-action originates from the granularity in the transfer of charges across a coherent conductor. As a result of Coulomb interactions, an excitation by these current pulses of the circuit electromagnetic modes is possible, which impedes the charge transfers and therefore reduces the conductance of the coherent conductor. This environmental Coulomb blockade is best understood in the limit of a tunnel junction embedded in a circuit of very high series impedance, which is of particular importance for single-electron devices 13 . In this limit, each time an electron tunnels across the junction, its charge stays a very long time on the capacitor C inherent to the junction's geometry. Consequently, a charging energy e 2 /2C has to be paid. As this energy is not available at low The bottom-left metal split gate (yellow) is used to tune the studied QPC. The outer-edge channel, shown as a red line, is partially transmitted at the QPC. A small ohmic contact labelled (red) is used to co...

Decoherence originates from the leakage of quantum information into external degrees of freedom. For a qubit, the two main decoherence channels are relaxation and dephasing. Here, we report an experiment on a superconducting qubit where we retrieve part of the lost information in both of these channels. We demonstrate that raw averaging the corresponding measurement records provides a full quantum tomography of the qubit state where all three components of the effective spin-1/2 are simultaneously measured. From single realizations of the experiment, it is possible to infer the quantum trajectories followed by the qubit state conditioned on relaxation and/or dephasing channels. The incompatibility between these quantum measurements of the qubit leads to observable consequences in the statistics of quantum states. The high level of controllability of superconducting circuits enables us to explore many regimes from the Zeno effect to underdamped Rabi oscillations depending on the relative strengths of driving, dephasing, and relaxation.

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Quantum physics emerge and develop as temperature is reduced. Although mesoscopic electrical circuits constitute an outstanding platform to explore quantum behaviour, the challenge in cooling the electrons impedes their potential. The strong coupling of such micrometre-scale devices with the measurement lines, combined with the weak coupling to the substrate, makes them extremely difficult to thermalize below 10 mK and imposes in situ thermometers. Here we demonstrate electronic quantum transport at 6 mK in micrometre-scale mesoscopic circuits. The thermometry methods are established by the comparison of three in situ primary thermometers, each involving a different underlying physics. The employed combination of quantum shot noise, quantum back action of a resistive circuit and conductance oscillations of a single-electron transistor covers a remarkably broad spectrum of mesoscopic phenomena. The experiment, performed in vacuum using a standard cryogen-free dilution refrigerator, paves the way towards the sub-millikelvin range with additional thermalization and refrigeration techniques.