Breakdown of the Wiedemann–Franz law in a unitary Fermi gas

Abstract

Heat and matter currents are required to relax an out-of-equilibrium system with temperature and chemical potential gradients to thermodynamical equilibrium. The ratio of heat to particle conductance characterizes this response and takes a universal value for typical electronic materials, known as the Wiedemann–Franz law, originating in the quasi-particle nature of the excitations contributing to transport. Investigating the transport dynamics between two reservoirs of ultracold and strongly interacting Fermi gases, connected by a quantum point contact, we observe a nonequilibrium steady state, strongly violating the Wiedemann–Franz law. This cold atom version of the fountain effect, previously observed in superfluid helium superleaks, is characterized by a weak coupling between heat and particle currents that results in a nonvanishing Seebeck coefficient. 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.