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arXiv:1805.05354 · Annual Review of Condensed Matter Physics

Universal Spin Transport and Quantum Bounds for Unitary Fermions

Tilman Enss, Joseph H. Thywissen

Published Nov 28, 2018• 41 citations
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Abstract

We review recent advances in experimental and theoretical understanding of spin transport in strongly interacting Fermi gases. The central new phenomenon is the observation of a lower bound on the (bare) spin diffusivity in the strongly interacting regime. Transport bounds are of broad interest for the condensed matter community, with a conceptual similarity to observed bounds in shear viscosity and charge conductivity. We discuss the formalism of spin hydrodynamics, how dynamics are parameterized by transport coefficients, the effect of confinement, the role of scale invariance, the quasiparticle picture, and quantum critical transport. We conclude by highlighting open questions, such as precise theoretical bounds, relevance to other phases of matter, and extensions to lattice systems.

DOI
10.1146/annurev-conmatphys-031218-013732

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We review recent advances in experimental and theoretical understanding of spin transport in strongly interacting Fermi gases. The central new phenomenon is the observation of a lower bound on the (bare) spin diffusivity in the strongly interacting regime. Transport bounds are of broad interest for the condensed matter community, with a conceptual similarity to observed bounds in shear viscosity and charge conductivity. We discuss the formalism of spin hydrodynamics, how dynamics are parameterized by transport coefficients, the effect of confinement, the role of scale invariance, the quasiparticle picture, and quantum critical transport. We conclude by highlighting open questions, such as precise theoretical bounds, relevance to other phases of matter, and extensions to lattice systems.
The experimental realization of stable, ultracold Fermi gases near a Feshbach resonance allows to study gases with attractive interactions of essentially arbitrary strength. They extend the classic paradigm of BCS into a regime which has never been accessible before. We review the theoretical concepts which have been developed in this context, including the Tan relations and the notion of fixed points at zero density, which are at the origin of universality. We discuss in detail the universal thermodynamics of the unitary Fermi gas which allows a fit free comparison between theory and experiment for this strongly interacting system. In addition, we adress the consequences of scale invariance at infinite scattering length and the subtle violation of scale invariance in two dimensions. Finally we discuss the Fermionic excitation spectrum accessible in momentum resolved RF-spectroscopy and the origin of universal lower bounds for the shear viscosity and the spin diffusion constant.
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.
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.
Understanding the quantum dynamics of strongly interacting fermions is a problem relevant to diverse forms of matter, including high-temperature superconductors, neutron stars, and quark-gluon plasma. An appealing benchmark is offered by cold atomic gases in the unitary limit of strong interactions. Here, we study the dynamics of a transversely magnetized unitary Fermi gas in an inhomogeneous magnetic field. We observe the demagnetization of the gas, caused by diffusive spin transport. At low temperatures, the diffusion constant saturates to the conjectured quantum-mechanical lower bound ≃ ħ/m, where m is the particle mass. The development of pair correlations, indicating the transformation of the initially noninteracting gas toward a unitary spin mixture, is observed by measuring Tan's contact parameter.
Transport in strongly correlated fermions cannot be understood by fermionic quasiparticles alone. We present a theoretical framework for quantum transport that incorporates strong local correlations of fermion pairs. These contact correlations add essential contributions to viscous, thermal and sound transport coefficients. The bulk viscosity, in particular, receives its dominant contribution from pair excitations. Moreover, it can be measured elegantly by observing the response to a time-dependent scattering length even when the fluid is not moving. Rapid changes of the scattering length drive the system far out of local equilibrium, and we show how it relaxes back to equilibrium following a hydrodynamic attractor before a Navier–Stokes description becomes valid. This paper summarizes a talk given at the Symposium “Open questions in the quantum many-body problem” at the Institut Henry Poincaré, Paris, in July 2024.
We address recent spin transport experiments in ultracold unitary Fermi gases. We provide a theoretical understanding for how the measured temperature dependence of the spin diffusivity at low TTT can disagree with the expected behavior of a Fermi liquid (FL), while the spin susceptiblity, following the experimental protocols, is consistent with a FL picture. We show that the experimental protocols for extracting the spin susceptibility implicitly reflect a FL viewpoint; relaxing this leads to consistency within but not proof of a pseudogap-based theory. Our transport calculations yield insight into the observed suppression of the spin diffusion constant at lower TTT.