Session T2: Invited Session: Transport in Degenerate Gases

Transverse Spin Diffusion

Transverse spin diffusion is a relatively new transport coefficient and a review of its history and physical basis will be presented. In NMR spin diffusion is often measured by spin echo techniques, which involve spin currents perpendicular to the direction of the magnetization, in contrast with the usual longitudinal case where the current is parallel to the magnetization. The first indication that this involved new physics was the Leggett-Rice effect (1970) in which spin waves, new spin-echo behavior, and an altered spin diffusion coefficient were predicted in liquid $^{3}$He. This effect gave the possibility of the first measurement of $F_{1}^{a}$, the parameter of the Landau Fermi-liquid theory mean-field responsible for the effect. In 1982 Lhuillier and Laloe found a transport equation very similar to the Leggett equation, but valid for highly-polarized dilute Boltzmann Bose and Fermi gases, and describing the ``identical spin rotation effect'' (ISRE), the analog of a Landau mean field. Coincidentally Bashkin and Meyerovich had also given equivalent descriptions of transport in polarized Boltzmann gases. That a mean-field effect could exists in dilute Boltzmann gases was theoretically surprising, but was confirmed experimentally. At low polarization the basic transverse diffusion constant $D_{\perp}$ coincides with the longitudinal value $D_{\parallel}$; however Meyerovich first pointed out that they could differ in highly polarized degenerate gases. Indeed detailed calculations (Jeon and Mullin) showed that, while $D_{\parallel}$ is proportional to $T^{-2}$, $D_{\perp}$ approaches a constant (depending on polarization) at low $T$. Considerable controversy existed until experimental verification was achieved in 2004. The importance of ISRE again arose in 2008 as the basis of ``anomalous spin-state segregation'' in Duke and JILA experiments. More recently application of the ideas of transverse spin diffusion to strongly interacting Fermi gases has resulted in the observation of the diffusion constants at the quantum limit where $D\sim\hbar/m.$   

From Terminal to Terminal with Atoms

We study fundamental concepts of particle and heat transport in a model system using ultracold atoms. It consists of a channel connecting two macroscopic reservoirs of fermionic lithium atoms. The channel can be switched from ballistic to diffusive, and it can be structured to form a quantum point contact or a quantum wire. Measurements of the thermoelectric effect and particle transport in the quantum regime will be presented. Our measurements find an ideal description in the Landauer-Buttiker formalism, which views conduction as the transport of carriers from one terminal to another.   

Transport in the quantum critical regime

In this talk I will explain the relevance of the quantum critical point for the phase diagram of the unitary Fermi gas, briefly review theoretical approaches, and present results for the shear viscosity and spin diffusion in strongly interacting Fermi gases. The unitary Fermi gas describes strongly interacting fermions ranging from ultracold atoms near a Feshbach resonance to dilute neutron matter, which share a common universal phase diagram. The behavior at finite temperature is governed by a quantum critical point (QCP) at zero temperature and zero density, and observables can be expressed by universal scaling functions of the distance from the critical point. In the quantum critical regime above the QCP, thermal and quantum fluctuations are equally important, and the absence of a small parameter makes the computation of critical properties demanding. I will mention two theoretical approaches to transport properties in this regime: the large-N expansion in the number of fermion flavors allows for a systematic and controlled expansion even at strong coupling and elucidates the importance of medium effects on scattering. Second, the Luttinger-Ward, or self-consistent T-matrix approach goes beyond the quasiparticle picture and also explains universal high-energy tails. I will present results on the shear viscosity, or internal friction, for mass transport and show that the strongly interacting Fermi gas is an almost perfect quantum fluid. On the other hand, if particles of different spin move in opposite directions, the dynamics are governed by spin diffusion. One can distinguish longitudinal diffusion, when atomic clouds of different spin collide, and transverse diffusion, when the magnetization is wound up in a helix in a spin-echo experiment. Medium scattering and spin rotation have a strong effect on spin diffusion, and I will discuss how spin transport becomes very slow at strong coupling in the quantum degenerate regime and reaches a quantum limit of diffusion.   

Thermoelectric transport in a two-dimensional Bose gas

We demonstrate a new scheme to extract particle and energy flow induced by temperature gradients; equivalent to ``thermoelectricity'' in electronic materials. From in situ images, we analyze the density and energy redistribution of two-dimensional Bose gases in the presence of three-body inelastic collisions. We determine the thermopower and the Lorenz number, both showing interesting behavior in the quantum degenerate regime. Thermopower changes sign suggesting the emergence of superfluid counterflow; the Lorenz number approaches zero, contrasting with the Wiedermann-Franz law.