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arXiv:1507.05975 · Physical Review A

Lattice Boltzmann simulations of a strongly interacting two-dimensional Fermi gas

Jasmine Brewer, Miller Mendoza, Ryan E. Young, Paul Romatschke

Published Jan 20, 2016• 26 citations
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Abstract

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.

DOI
10.1103/physreva.93.013618

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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.
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We consider the time evolution of a dilute atomic Fermi gas after release from a trapping potential. A common difficulty with using fluid dynamics to study the expansion of the gas is that the theory is not applicable in the dilute corona, and that a naive treatment of the entire cloud using fluid dynamics leads to unphysical results. We propose to remedy this problem by including certain nonhydrodynamic degrees of freedom, in particular anisotropic components of the pressure tensor, in the theoretical description. We show that, using this method, it is possible to describe the crossover from fluid dynamics to ballistic expansion locally. We illustrate the use of anisotropic fluid dynamics by studying the expansion of the dilute Fermi gas at unitarity using different functional forms of the shear viscosity, including a shear viscosity that is solely a function of temperature, $\ensuremath{\eta}\ensuremath{\sim}{(mT)}^{3/2}$, as predicted by kinetic theory in the dilute limit.
The shear viscosity of a two-dimensional Fermi gas interacting via a short-range potential with scattering length a2d{a}_{2\mathrm{d}}a2d​ in kinetic theory is computed. It is found that classical kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two-dimensional gas is comparable to that of the three-dimensional unitary gas. Results are applied to the damping of collective modes of a trapped Fermi gas, and compared to experimental data recently obtained by Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)].
We study the validity range of the semiclassical Boltzmann equation in describing the dynamics of two-dimensional Fermi gas. Here we numerically solve the Boltzmann equation based on the relaxation-time approximation. By comparing the numerically extracted damping of the quadrupole mode with the experimental data reported in Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)], we demonstrate that the Boltzmann equation is applicable at least when the temperature is larger than 0.47TF0.47{T}_{F}0.47TF​, up to the strong coupling regime, where TF{T}_{F}TF​ is the Fermi temperature.
This thesis considers out-of-equilibrium dynamics of strongly interacting non-relativistic Fermi gases in several two and three dimensional geometries. The tools of second-order hydrodynamics and gauge-gravity duality will be utilized to address this system. Many of the themes of this work are motivated by the observed similarities in transport properties between strongly interacting Fermi gases and other very different strongly interacting quantum fluids such as the quark-gluon plasma, high temperature superconductors, and quantum field theories described by gauge-gravity duality. In particular, these systems all nearly saturate the conjectured lower bound on the ratio of shear viscosity to entropy density η/s≥ℏ/(4πkB)η/s \geq \hbar/(4 πk_B)η/s≥ℏ/(4πkB​) coming from the AdS/CFT correspondence. Among other things, this observation, in conjunction with current experiment and data analysis in atomic, condensed matter, and nuclear physics lends itself to the following questions: How perfect of a fluid is the strongly interacting Fermi gas, and can one find a more stringent constraint on η/sη/sη/s in Fermi gases? Do the similarities in transport properties among strongly interacting quantum systems extend beyond dynamics controlled by the hydrodynamical shear viscosity? In regards to the first question, by utilizing second-order hydrodynamics, it will be demonstrated that higher-order collective modes of a harmonically trapped Fermi gas may serve as a more sensitive probe of the shear viscosity. For the second question, both second-order hydrodynamics and a gravity dual theory are used to make predictions about dynamics occurring on short timescales where hydrodynamics is expected to break down. In particular the appearance of a class of "non-hydrodynamic" collective modes not contained within a Navier-Stokes description of the strongly interacting Fermi gas will be discussed.
We study the transition from the hydrodynamic to the collisionless regime in collective modes of three- and two-dimensional Fermi gases by using the semiclassical Boltzmann equation. We use direct numerical simulations as well as the method of phase-space moments to solve the Boltzmann equation and show that the restriction to second-order moments is not accurate enough. By including higher-order moments, we can successfully describe the hydrodynamic to collisionless transition observed in the quadrupole mode in three-dimensional Fermi gases and the frequency shift and damping of the sloshing mode due to the anharmonic shape of the experimental trap potential. In the case of two-dimensional Fermi gases, however, the strong damping of the quadrupole mode observed in a recent experiment remains unexplained.