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arXiv:1605.00014 · Physical Review A

String-theory-based predictions for nonhydrodynamic collective modes in strongly interacting Fermi gases

H. Bantilan, Jasmine Brewer, Takaaki Ishii, William E. Lewis, Paul Romatschke

Published Sep 19, 2016• 20 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.94.033621

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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.
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.
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.
In this thesis we present fully nonlinear dissipative hydrodynamics simulations using the lattice Boltzmann method which we have developed to study hydrodynamics in cold atomic gases. We motivate and derive the specifics of the lattice Boltzmann implementation for this system, and then use our simulations to study collective oscillations in two-dimensional Fermi gases. We show that all dominant frequencies and damping rates of the breathing and quadrupole oscillatory modes agree quantitatively with analytic solutions in the hydrodynamic limit for a gas with ideal equation of state in a harmonic trap. We suggest improvements to our numerical methods which we expect to improve the quantitative agreement of the quadrupole mode frequency with the expected value outside of the hydrodynamic limit. We also suggest techniques for extracting the non-dominant (non-hydrodynamic) damping rate of the quadrupole mode in the hydrodynamic regime with higher precision. Additionally, we propose that the observed non-hydrodynamic damping of the quadrupole mode would be interesting to study experimentally for applications to collective oscillations in the quark-gluon plasma.
Unitary fermi gases have been widely studied as they provide a tabletop archetype for research on strongly coupled many body systems and perfect fluids. Research into unitary fermi gases can provide insight into may other strongly interacting systems including high temperature superconductor, quark-gluon plasmas, and neutron stars. Within the unitary regime, the equilibrium transport coefficients and thermodynamic properties are universal functions of density and temperature. Thus, unitary fermi gases provide a archetype to study nonperturbative many-body physics, which is of fundamental significance and crosses several fields.\nThis thesis reports on two topics regarding unitary fermi gases. A recent string theory conjecture gives a lower bound for the dimensionless ratio of shear viscosity of entropy, η=s ≥ 4πℏ =kb. Unitary fermi gases are a candidate for prefect fluids, yet η=s is well above the string theory bound. Using a stochastic formulation of hydrodynamics, we calculate a lower bound for this ratio accounting for the momentum dissipation from fluctuations. This lower bound is in good agreement with both theoretical and experimental results.\nThe second question addressed is the simulation of elliptic flow. Elliptic flow, first observed in 2002, is a characteristic of strongly coupled systems and has been studied in both quark-gluon plasmas and unitary fermi gases. As such, simulations of these systems are of interest. We test a variety of lattice Boltzmann models and compare the simulation results to the theoretical and experimental findings.
We suggest that collective oscillation frequencies of cold trapped gases can be used to test predictions from quantum many-body physics. Our motivation lies in both rigid experimental tests of theoretical calculations and a possible improvement of measurements of particle number, chemical potential or temperature. We calculate the effects of interaction, dimensionality and thermal fluctuations on the collective modes of a dilute Bose gas in the hydrodynamic limit. The underlying equation of state is provided by the non-perturbative Functional Renormalization Group or by Lee–Yang theory. The spectrum of oscillation frequencies could be measured by response techniques. Our findings are generalized to bosonic or fermionic quantum gases with an arbitrary equation of state in the two-fluid hydrodynamic regime. For any given equation of state P (μ, T ) and normal fluid density n n (μ, T ), the collective oscillation frequencies in a d -dimensional isotropic potential are found to be the eigenvalues of an ordinary differential operator. We suggest a method of numerical solution and discuss the zero-temperature limit. Exact results are provided for harmonic traps and certain special forms of the equation of state. We also present a phenomenological treatment of dissipation effects and discuss the possibility of exciting the different eigenmodes individually.
At finite temperature, the hydrodynamic collective modes of superfluid trapped Fermi gases are coupled to the motion of the normal component, which in the BCS limit behaves like a collisionless normal Fermi gas. The coupling between the superfluid and the normal components is treated in the framework of a semiclassical transport theory for the quasiparticle-distribution function, combined with a hydrodynamic equation for the collective motion of the superfluid component. We develop a numerical test-particle method for solving these equations in the linear-response regime. As a first application we study the temperature dependence of the collective quadrupole mode of a Fermi gas in a spherical trap. The coupling between the superfluid collective motion and the quasiparticles leads to a rather strong damping of the hydrodynamic mode already at very low temperatures. At higher temperatures the spectrum has a two-peak structure, the second peak corresponding to the quadrupole mode in the normal phase.