In a mesoscopic conductor, electric resistance is detected even if the device is defect-free. We engineered and studied a cold-atom analog of a mesoscopic conductor. It consists of a narrow channel connecting two macroscopic reservoirs of fermions that can be switched from ballistic to diffusive. We induced a current through the channel and found ohmic conduction, even when the channel is ballistic. We measured in situ the density variations resulting from the presence of a current and observed that density remains uniform and constant inside the ballistic channel. In contrast, for the diffusive case with disorder, we observed a density gradient extending through the channel. Our approach opens the way toward quantum simulation of mesoscopic devices with quantum gases.

Thermoelectric effects, such as the generation of a particle current by a temperature gradient, have their origin in a reversible coupling between heat and particle flows. These effects are fundamental probes for materials and have applications to cooling and power generation. Here we demonstrate thermoelectricity in a fermionic cold atoms channel, ballistic or diffusive, connected to two reservoirs. We show that the magnitude of the effect and the efficiency of energy conversion can be optimized by controlling the geometry or disorder strength. Our observations are in quantitative agreement with a theoretical model based on the Landauer-Büttiker formalism. Our device provides a controllable model-system to explore mechanisms of energy conversion and realizes a cold atom based heat engine. PACS numbers:In general, heat and particle transport are coupled processes [1]. This coupling leads to thermoelectric effects, such as a Seebeck voltage drop in a conductor subject to a thermal gradient. These effects are important for probing elementary excitations in materials, for example, giving access to the sign of charge carriers [2]. Moreover, they have practical applications to refrigeration, and power generation from waste-heat recovery [3,4]. Recently, there has also been interest in thermoelectric effects in nano-and molecular-scale electronic devices [5,6]. The progress in modeling solid-state physics with cold atoms [7,8] raises the question whether thermoelectricity can be observed in such a controlled setting [9,10], where set-ups analogous to mesoscopic devices were realized [11][12][13]. Whilst the thermodynamic interplay between thermal and density collective modes has been seen in a second sound experiment [14], thermoelectric effects have so far not been investigated.Here, we demonstrate a cold atoms device in which a particle current is generated by a temperature bias. We prepare a mesoscopic channel connecting two atomic reservoirs having equal particle numbers. Heating one of the reservoirs establishes a temperature bias and the compressible cloud forming the hot reservoir expands. Hence, one naively expects an initial particle flow from the cold denser side to the hot. In contrast, we observe the opposite effect: a net particle current initially directed from the hot to the cold side. This is a direct manifestation of the intrinsic thermoelectric power of the channel. The temperature bias leads to a current of highenergy particles from hot to cold and a current of lowenergy particles from cold to hot. In our channel, particles are transported at a rate which increases with energy, leading to an asymmetry between the high-energy and low-energy particle currents. This results in a total current from hot to cold, which overcomes the thermodynamic effect of the reservoirs. Hence, work is performed by carrying atoms from lower to higher chemical potential, and our system can be regarded as a cold-atoms based heat engine.A schematic view of the experimental setup is shown in figure 1A. It is based on our pre...

In transport experiments the quantum nature of matter becomes directly evident when changes in conductance occur only in discrete steps [1], with a size determined solely by Planck's constant h. The observations of quantized steps in the electric conductance [2,3] have provided important insights into the physics of mesoscopic systems [4] and allowed for the development of quantum electronic devices [5]. Even though quantized conductance should not rely on the presence of electric charges, it has never been observed for neutral, massive particles [6]. In its most fundamental form, the phenomenon requires a quantum degenerate Fermi gas, a ballistic and adiabatic transport channel, and a constriction with dimensions comparable to the Fermi wavelength. Here we report on the observation of quantized conductance in the transport of neutral atoms. We employ high resolution lithography to shape light potentials that realize either a quantum point contact or a quantum wire for atoms. These constrictions are imprinted on a quasi two-dimensional ballistic channel connecting two adjustable reservoirs of quantum degenerate fermionic lithium atoms [7]. By tuning either a gate potential or the transverse confinement of the constrictions, we observe distinct plateaus in the conductance for atoms. The conductance in the first plateau is found to be equal to 1/h, the universal conductance quantum. For low gate potentials we find good agreement between the experimental data and the Landauer formula, with all parameters determined a priori. Our experiment constitutes the cold atom version of a mesoscopic device and can be readily extended to more complex geometries and interacting quantum gases.As pointed out by Landauer in 1957, conductance is the transmission of carriers from one terminal to another [8,9]. If the carriers move adiabatically through the channel connecting the terminals, each of its transverse modes contributes with 1/h to the conductancewhere f is the Fermi-Dirac distribution, E n the energy of the n-th transverse mode, and µ the chemical potential in the two terminals at equilibrium. When the temperature is sufficiently low compared to the transverse energy level spacing, the contribution of individual modes can be isolated in a transport measurement, leading to quantized plateaus in the conductance. Whilst ubiquitous in electronics, a two-terminal setup for atomic gases has only recently been demonstrated. Here, neutral atom currents play the role of electric currents and they are driven by a chemical potential bias rather than an electric voltage, a situation corresponding to ideal charge screening. Until now, the conductance of quasi two-dimensional multimode channels was measured, probing ballistic, diffusive and superfluid regimes [7,10,11]. Yet, in order to identify the contribution of an individual mode to the transport, a tightly confining channel geometry is required in which the energy separation between individual transverse modes is large compared to the temperature [12]. This requirement is also enc...

The ability of particles to flow with very low resistance is characteristic of superfluid and superconducting states, leading to their discovery in the past century. Although measuring the particle flow in liquid helium or superconducting materials is essential to identify superfluidity or superconductivity, no analogous measurement has been performed for superfluids based on ultracold Fermi gases. Here we report direct measurements of the conduction properties of strongly interacting fermions, observing the well-known drop in resistance that is associated with the onset of superfluidity. By varying the depth of the trapping potential in a narrow channel connecting two atomic reservoirs, we observed variations of the atomic current over several orders of magnitude. We related the intrinsic conduction properties to the thermodynamic functions in a model-independent way, by making use of high-resolution in situ imaging in combination with current measurements. Our results show that, as in solid-state systems, current and resistance measurements in quantum gases provide a sensitive probe with which to explore many-body physics. Our method is closely analogous to the operation of a solid-state field-effect transistor and could be applied as a probe for optical lattices and disordered systems, paving the way for modelling complex superconducting devices.

FIG. 3 (color online). B parameter (see text)as a function of disorder strength. The green dotted line represents the percolation threshold of the speckle potential, and coincides with the change of behavior from superfluid to single-particle transport. The dash-dotted line shows the correlation energy E σ . Error bars represent statistical errors.