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arXiv:1508.01199 · Physical Review Letters

Nonhydrodynamic Transport in Trapped Unitary Fermi Gases

Jasmine Brewer, Paul Romatschke

Published Nov 5, 2015• 37 citations
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Abstract

Many strongly coupled fluids are known to share similar hydrodynamic transport properties. In this work we argue that this similarity could extend beyond hydrodynamics to transient dynamics through the presence of nonhydrodynamic modes. We review nonhydrodynamic modes in kinetic theory and gauge-gravity duality and discuss their signatures in trapped Fermi gases close to unitarity. Reanalyzing previously published experimental data we find hints of nonhydrodynamic modes in cold Fermi gases in two and three dimensions.

DOI
10.1103/physrevlett.115.190404

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Many strongly coupled fluids are known to share similar hydrodynamic transport properties. In this work we argue that this similarity could extend beyond hydrodynamics to transient dynamics through the presence of nonhydrodynamic modes. We review nonhydrodynamic modes in kinetic theory and gauge-gravity duality and discuss their signatures in trapped Fermi gases close to unitarity. Reanalyzing previously published experimental data we find hints of nonhydrodynamic modes in cold Fermi gases in two and three dimensions.
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Very different strongly interacting quantum systems such as Fermi gases, quark-gluon plasmas formed in high-energy ion collisions, and black holes studied theoretically in string theory are known to exhibit quantitatively similar damping of hydrodynamic modes. It is not known if such similarities extend beyond the hydrodynamic limit. Do nonhydrodynamic collective modes in Fermi gases with strong interactions also match those from string theory calculations? In order to answer this question, we use calculations based on string theory to make predictions for modes outside the hydrodynamic regime in trapped Fermi gases. These predictions are amenable to direct testing with current state-of-the-art cold atom experiments.
We present the results of a variational calculation of the frequencies of the low-lying Landau two-fluid hydrodynamic modes in a trapped Fermi superfluid gas at unitarity. Landau's two-fluid hydrodynamics is expected to be the correct theory of Fermi superfluids at finite temperatures close to unitarity, where strong interactions give rise to collisional hydrodynamics. Two-fluid hydrodynamics predicts the existence of in-phase modes in which the superfluid and normal fluid components oscillate together, as well as out-of-phase modes where the two components move against each other. We prove that, at unitarity, the dipole and breathing in-phase modes are locally isentropic. Their frequencies are independent of temperature and are the same above and below the superfluid transition, a feature due as much to the harmonic trapping potential as to the thermodynamic properties at unitarity. The out-of-phase modes, in contrast, are strongly dependent on temperature and hence can be used to test the thermodynamic properties and superfluid density of a Fermi gas at unitarity. We give numerical results for the frequencies of these modes as function of temperature in an isotropic trap at unitarity.
Strongly interacting two-component Fermi gases have become a powerful tool for studying many-body physics. The interactions between the components can be varied widely, allowing the full crossover from BCS to BEC superfluids to be explored. In the strong interaction region at unitarity, the behaviour of the system becomes independent of microscopic details of the interaction. Hence, these Fermi gases can be used as a testing ground for microscopic theories of strongly-interacting Fermi matter. We propose that the out-of-phase two-fluid modes can be excited and measured in a two-photon Bragg scattering experiment, which measures the density response function. We investigate the structure of the two-fluid density response function at unitarity within our variational approach. The out-of-phase modes are found to have appreciable weight at intermediate temperatures in the superfluid phase and should be observable in Bragg scattering experiments. In this thesis, we study the Landau two-fluid hydrodynamic modes of a trapped Fermi gas superfluid, including the "out-of-phase" oscillations of the superfluid and normal fluid components. These modes are the analogue of second sound in superfluid 4He, and have so far not been observed in trapped Fermi gas superfluids. An important part of this thesis is the development of a new variational method of solving the two-fluid equations for gases confined in a harmonic trap. The solution of the resulting algebraic equations for the two-fluid mode frequencies requires detailed knowledge of the local thermodynamic quantities in a trap. In contrast to "classical" BCS and BEC superfluids such as 3He and 4He, both fermionic and bosonic thermal excitations contribute significantly to the thermodynamics close to unitarity. The fact that these excitations are coupled at finite temperatures means that one cannot write down simple expressions for thermodynamic quantities in terms of the spectrum of these excitations. Our calculations of thermodynamic quantities involve essentially ab initio calculations based on the microscopic theory developed by Nozieres and Schmitt-Rink, applied to a nonuniform trapped gas using a local density approximation.
We present fully nonlinear dissipative fluid dynamics simulations of a strongly interacting trapped two-dimensional Fermi gas using a lattice Boltzmann algorithm. We are able to simulate nonharmonic trapping potentials, temperature-dependent viscosities, as well as a discretized version of the ballistic (noninteracting) behavior. Our approach lends itself to direct comparison with experimental data, opening up the possibility of a precision determination of transport coefficients in the strongly interacting Fermi gas. Furthermore, we predict the presence of a strongly damped (``nonhydrodynamic'') component in the quadrupole mode, which should be observable experimentally.
We present a proposal to measure anisotropic shear viscosity in a strongly interacting, ultra-cold, unitary Fermi gas confined in a harmonic trap. We introduce anisotropy in this setup by strongly confining the gas in one of the directions with relatively weak confinement in the remaining directions. This system has a close resemblance to anisotropic strongly coupled field theories studied recently in the context of gauge-gravity duality. Computations in such theories (which have gravity duals) revealed that some of the viscosity components of the anisotropic shear viscosity tensor can be made much smaller than the entropy density, thus parametrically violating the bound proposed by Kovtun, Son and Starinets (KSS): ηs≥14π\frac η {s} \geq \frac{1}{4 π}sη​≥4π1​. A Boltzmann analysis performed in a system of weakly interacting particles in a linear potential also shows that components of the viscosity tensor can be reduced. Motivated by these exciting results, we propose two hydrodynamic modes in the unitary Fermi gas whose damping is governed by the component of shear viscosity expected to violate the KSS bound. One of these modes is the well known scissor mode. We estimate trap parameters for which the reduction in the shear viscosity is of order unity and find that the trap geometry, the damping timescales, and mode amplitudes are within the range of existing experimental setups on ultra-cold Fermi gases.