[Paper Review] A Proposal for measuring Anisotropic Shear Viscosity in Unitary Fermi Gases

Rickmoy Samanta, Rishi Sharma+1 more|arXiv (Cornell University)|Nov 8, 2016

Quantum, superfluid, helium dynamics3 citations

TL;DR

This paper proposes measuring anisotropic shear viscosity in a unitary Fermi gas by engineering anisotropic harmonic trapping, where strong confinement in one direction induces viscosity components that may parametrically violate the KSS bound. Using hydrodynamic modes—particularly the scissor mode—under experimentally feasible parameters (e.g., ωz ≈ 2π×77,000 rad/s), the study predicts a significant reduction in ηxz, with damping timescales and amplitudes within current experimental reach.

ABSTRACT

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): $\frac η {s} \geq \frac{1}{4 π}$. 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.

Motivation & Objective

• To propose a feasible experimental setup for measuring anisotropic shear viscosity in strongly correlated ultra-cold Fermi gases.
• To identify hydrodynamic modes—specifically the scissor mode and elliptic mode—whose damping is sensitive to viscosity components expected to violate the KSS bound.
• To demonstrate that trap parameters such as increased transverse confinement (ωz) can induce a significant reduction in ηxz, approaching or exceeding order-unity suppression.
• To bridge theoretical predictions from gravity duals in anisotropic field theories with experimental observables in trapped ultracold Fermi gases.

Proposed method

• Engineer anisotropic harmonic trapping with strong confinement in one direction (z) and weaker confinement in the transverse plane (x,y), creating a system analogous to anisotropic strongly coupled field theories.
• Use the local density approximation (LDA) to model the harmonic potential as approximately linear in the region where viscosity is probed, enabling analytical treatment of transport coefficients.
• Apply Boltzmann transport theory in the weak-coupling regime to compute corrections to shear viscosity, particularly ηxz, under a linear potential.
• Identify the scissor mode and elliptic mode as hydrodynamic probes whose damping rates depend on the anisotropic viscosity component ηxz.
• Estimate trap parameters (e.g., μ = 10 μK, T = Tc/2, ωz ≈ 2π×77,000 rad/s) where the dimensionless parameter κ_LDA ≈ 1, signaling strong deviation from isotropy.
• Compare predicted damping timescales and mode amplitudes with existing experimental data (e.g., Phys. Rev. Lett. 99, 150403) to confirm feasibility.

Experimental results

Research questions

• RQ1 Can anisotropic shear viscosity components in a unitary Fermi gas be experimentally probed via hydrodynamic modes?
• RQ2 To what extent can the viscosity component ηxz be reduced below the KSS bound in a trapped ultracold Fermi gas with engineered anisotropy?
• RQ3 What trap parameters (e.g., ωz, chemical potential, temperature) are required to achieve a measurable suppression of ηxz?
• RQ4 How do the damping rates of the scissor mode and elliptic mode depend on the anisotropic viscosity tensor?
• RQ5 Can the observed damping in existing experiments be used as a baseline to detect parametric viscosity suppression in more anisotropic traps?

Key findings

• For μ = 10 μK, T = Tc/2 (Tc ≈ 0.4μ), and ωz ≈ 2π×77,000 rad/s, the dimensionless parameter κ_LDA ≈ 1, indicating a regime where viscosity suppression is expected.
• The Boltzmann analysis predicts an order-unity reduction in the ηxz component of the shear viscosity tensor under these conditions.
• The damping time of the scissor mode remains experimentally accessible (~1 ms) even as ωz is increased, preserving observability.
• The maximum angular amplitude of the scissor mode is reduced to θ_max ≈ 28°, still within the observable range of current experiments.
• The predicted reduction in ηxz is consistent with theoretical expectations from gravity duals in anisotropic black brane backgrounds, suggesting a bridge between holography and cold atom experiments.
• Gradual increase in ωz from 2π×10⁴ to 2π×77,000 rad/s allows for a measurable trend in viscosity suppression, enabling systematic experimental verification.