Two-fluid hydrodynamic modes in a trapped superfluid gas

TL;DR

This paper develops a simplified variational method to analyze two-fluid hydrodynamic modes in trapped superfluid gases across the BCS-BEC crossover, including the unitarity region, extending previous models for Bose gases.

Contribution

It introduces a new variational formulation for two-fluid hydrodynamic modes in superfluid gases, applicable across the entire BCS-BEC crossover, simplifying the analysis compared to traditional differential equation approaches.

Findings

Derives mode frequencies from algebraic equations involving thermodynamic derivatives.

Reduces to known results for pure superfluids at zero temperature.

Provides a more physical and simpler method for studying superfluid hydrodynamics.

Abstract

In the collisional region at finite temperatures, the collective modes of superfluids are described by the Landau two-fluid hydrodynamic equations. This region can now be probed over the entire BCS-BEC crossover in trapped Fermi superfluids with a Feshbach resonance, including the unitarity region. Building on the approach initiated by Zaremba, Nikuni, and Griffin in 1999 for trapped atomic Bose gases, we present a new variational formulation of two-fluid hydrodynamic collective modes based on the work of Zilsel in 1950 developed for superfluid helium. Assuming a simple variational ansatz for the superfluid and normal fluid velocities, the frequencies of the hydrodynamic modes are given by solutions of coupled algebraic equations, with constants only involving spatial integrals over various equilibrium thermodynamic derivatives. This variational approach is both simpler and more physical than a direct attempt to solve the Landau two-fluid differential equations. Our two-fluid results are shown to reduce to those of Pitaevskii and Stringari for a pure superfluid at T=0.