Shear Viscosity of Uniform Fermi Gases with Population Imbalance

Weimin Cai,Hao Guo,Chih-Chun Chien,Yan He

doi:10.1038/s41598-018-22273-1

Weimin Cai, Hao Guo + Show 2 more

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https://doi.org/10.1038/s41598-018-22273-1

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Abstract

The shear viscosity has been an important topic in ultracold Fermi gases, and it has served as a diagnostic of various theories. Due to the complicated phase structures of population-imbalanced (polarized) Fermi gases with tunable attraction, past works on the shear viscosity mainly focused on unpolarized Fermi gases. Here we investigate the shear viscosity of homogeneous, population-imbalanced Fermi superfluid at finite temperatures by a pairing fluctuation theory for thermodynamical quantities and a gauge-invariant linear response theory for transport coefficients. The Cooper pairs lead to the anomalous shear viscosity analogous to the shear viscosity. We derive an exact relation connecting certain thermodynamic quantities and transport coefficients at the mean-field level for polarized unitary Fermi superfluids. An approximate relation beyond mean-field is proposed and only exhibits mild deviations from our numerical results. In the unitary and Bose-Einstein condensation (BEC) regimes, the total shear viscosity increases with the polarization because the excess majority fermions cause gapless excitations acting like a normal fluid. Moreover, competition among the excess fermions, noncondensed pairs, and fermionic quasiparticles may lead to non-monotonic behavior of the ratio between the shear viscosity and relaxation time as the polarization increases.

Highlights

We integrate the thermodynamics from a pairing theory of a fermionic superfluid beyond the mean-field BCS theory and the transport coefficients from a gauge-invariant linear response theory called the consistent fluctuation of order parameter (CFOP) theory[35,36]
The contributions from noncondensed pairs are included by a pairing-fluctuation theory applicable to polarized Fermi gases in the BCS-Bose-Einstein condensation (BEC) crossover
The ratio between the total shear viscosity and relaxation time increases with temperature and polarization, but competitions between the condensed and noncondensed pairs, fermionic quasiparticles, and excess fermions may lead to local maximum or minimum of (η + χ)/τ in the unitary limit or shallow BEC regimes as p increases

Summary

Introduction

Ultracold atomic Fermi gases provide versatile quantum simulators for complex many-particle systems, and their transport properties have attracted broad research interest[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. The studies of population-imbalanced Fermi gases are more difficult since at low temperatures phase separation of paired and unpaired fermions can emerge[28,30]. The “intermediate-temperature superfluid” describes where homogeneous polarized superfluids appear[32] when a population-imbalanced ultracold Fermi gas undergoes the BCS-Bose Einstein condensation (BEC) crossover as the attractive interaction increases[33]. A theoretical study of the shear viscosity of ultracold atomic Fermi superfluid with population imbalance will be presented here. In the unitary and BEC regimes, preformed (noncondensed) pairs emerge at finite temperatures due to strongly attractive interactions, but they do not contribute to superfluidity. The shear viscosity should include both the fermionic and bosonic (from the noncondensed pairs) contributions in the strongly attractive regime[43]. Similar to the shear viscosity from the energy-momentum tensor response function43. (See the Supplemental Information.) The total shear viscosity of polarized Fermi superfluids should include all the contributions, and we will show how a competition between the excess majority fermions and various excitations affect the ratio between the viscosity and relaxation time

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Conclusion