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...
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