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arXiv:1410.5841 · Physical Review A

Violation of the Wiedemann-Franz law for one-dimensional ultracold atomic gases

Michele Filippone, F. W. J. Hekking, Anna Minguzzi

Published Jan 5, 2016• 26 citations
arXivHTMLPDF

Abstract

We study energy and particle transport for one-dimensional strongly interacting bosons through a ballistic single channel connecting two atomic reservoirs. We show the emergence of particle- and energy-current separation, leading to the violation of the Wiedemann-Franz law. As a consequence, we predict different time scales for the equilibration of temperature and particle imbalances between the reservoirs. Going beyond the linear spectrum approximation, we show the emergence of thermoelectric effects, which could be controlled by either tuning interactions or the temperature. Our results describe, in a unified picture, fermions in condensed-matter devices and bosons in ultracold atom setups. We conclude by discussing the effects of a controllable disorder.

DOI
10.1103/physreva.93.011602

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We study energy and particle transport for one-dimensional strongly interacting bosons through a ballistic single channel connecting two atomic reservoirs. We show the emergence of particle- and energy-current separation, leading to the violation of the Wiedemann-Franz law. As a consequence, we predict different time scales for the equilibration of temperature and particle imbalances between the reservoirs. Going beyond the linear spectrum approximation, we show the emergence of thermoelectric effects, which could be controlled by either tuning interactions or the temperature. Our results describe, in a unified picture, fermions in condensed-matter devices and bosons in ultracold atom setups. We conclude by discussing the effects of a controllable disorder.
We report on coupled heat and particle transport measurements through a quantum point contact (QPC) connecting two reservoirs of resonantly interacting, finite temperature Fermi gases. After heating one of them, we observe a particle current flowing from cold to hot. We monitor the temperature evolution of the reservoirs and find that the system evolves after an initial response into a nonequilibrium steady state with finite temperature and chemical potential differences across the QPC. In this state any relaxation in the form of heat and particle currents vanishes. From our measurements we extract the transport coefficients of the QPC and deduce a Lorenz number violating the Wiedemann-Franz law by one order of magnitude, a characteristic persisting even for a wide contact. In contrast, the Seebeck coefficient takes a value close to that expected for a noninteracting Fermi gas and shows a smooth decrease as the atom density close to the QPC is increased beyond the superfluid transition. Our work represents a fermionic analog of the fountain effect observed with superfluid helium and poses challenges for microscopic modeling of the finite temperature dynamics of the unitary Fermi gas.
A gas of interacting ultracold fermions can be tuned into a strongly interacting regime using a Feshbach resonance. Here, we theoretically study quasiparticle transport in a system of two reservoirs of interacting ultracold fermions on the BCS side of the BCS-BEC crossover coupled weakly via a tunnel junction. Using the generalized BCS theory, we calculate the time evolution of the system that is assumed to be initially prepared in a nonequilibrium state characterized by a particle number imbalance or a temperature imbalance. A number of characteristic features like sharp peaks in quasiparticle currents or transitions between the normal and superconducting states are found. We discuss signatures of the Seebeck and the Peltier effects and the resulting temperature difference of the two reservoirs as a function of the interaction parameter ${({k}_{F}a)}^{\ensuremath{-}1}$. The Peltier effect may lead to an additional cooling mechanism for ultracold fermionic atoms.
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 in the ballistic and diffusive regimes, 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.
We propose experimental protocols to reveal thermoelectric and thermal effects in the transport properties of ultracold fermionic atoms, using the two-terminal setup recently realized at ETH. We show in particular that, for two reservoirs having equal particle numbers but different temperatures initially, the observation of a transient particle number imbalance during equilibration is a direct evidence of thermoelectric (off-diagonal) transport coefficients. This is a time-dependent analogue of the Seebeck effect, and a corresponding analogue of the Peltier effect can be proposed. We reveal that in addition to the thermoelectric coupling of the constriction a thermoelectric coupling also arises due to the finite dilatation coefficient of the reservoirs. We present a theoretical analysis of the protocols, and assess their feasibility by estimating the corresponding temperature and particle number imbalances in realistic current experimental conditions.
The transport properties of strongly interacting fermionic systems can reveal exotic states of matter, but experiments and theory have predominantly focused on bulk systems in the hydrodynamic limit describable with linear response coefficients such as electrical and thermal conductivity. In a ballistic channel connecting two superfluid reservoirs, recent experiments revealed a far-from-equilibrium regime beyond linear hydrodynamics where particle and entropy currents respond nonlinearly to biases of chemical potential and temperature, and their ratio is robust to the channel geometry. However, the origin of this robustness and its relation to the strong interparticle interactions remain unknown. Here, we study the coupled transport of particles and entropy tuning the interaction across the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS-BEC) crossover, the reservoir degeneracy across the superfluid phase transition, as well as the local potentials and confinement of the channel. Surprisingly, the entropy advectively transported per particle depends only on the interactions and reservoir degeneracy and not on the details of the channel, suggesting that this property has its origin in the universal equilibrium properties of the reservoirs. In contrast, the magnitudes of the advective and diffusive entropy currents vary significantly with the channel details. The advective current increases monotonically towards the BEC side, which can be largely explained by the estimated superfluid gap in the channel. The Wiedemann-Franz law that links the advective and diffusive currents in Fermi liquids is most egregiously violated at unitarity, suggesting a change in the nature of the excitations responsible for entropy diffusion near unitarity. These observations pose fundamental questions regarding transport phenomena in strongly interacting Fermi systems far from equilibrium.
We analyze the equilibration process between two either fermionic or bosonic reservoirs containing ultracold atoms with a fixed total number of particles that are weakly connected via a few-level quantum system. We allow for both the temperatures and particle densities of the reservoirs to evolve in time. Subsequently, linearizing the resulting equations enables us to characterize the equilibration process and its time scales in terms of equilibrium reservoir properties and linear-response transport coefficients. Additionally, we investigate the use of such a device as particle transistor or particle capacitor and analyze its efficiency.