Variational theory of two-fluid hydrodynamic modes at unitarity

TL;DR

This paper uses a variational approach to analyze low-lying two-fluid hydrodynamic modes in a trapped Fermi superfluid at unitarity, revealing temperature-independent in-phase modes and temperature-dependent out-of-phase modes.

Contribution

It provides the first variational calculation of two-fluid mode frequencies at unitarity, highlighting the distinct behaviors of in-phase and out-of-phase modes with temperature.

Findings

In-phase modes are locally isentropic with frequencies independent of temperature.

Out-of-phase modes vary strongly with temperature and can probe superfluid properties.

Numerical results for mode frequencies as a function of temperature are provided.

Abstract

We present the results of a variational calculation of the frequencies of the low-lying Landau two-fluid hydrodynamic modes in a trapped Fermi superfluid gas at unitarity. Landau's two-fluid hydrodynamics is expected to be the correct theory of Fermi superfluids at finite temperatures close to unitarity, where strong interactions give rise to collisional hydrodynamics. Two-fluid hydrodynamics predicts the existence of in-phase modes in which the superfluid and normal fluid components oscillate together, as well as out-of-phase modes where the two components move against each other. We prove that at unitarity, the dipole and breathing in-phase modes are locally isentropic. Their frequencies are independent of temperature and are the same above and below the superfluid transition. The out-of-phase modes, in contrast, are strongly dependent on temperature and hence, can be used to test the thermodynamic properties and superfluid density of a Fermi gas at unitarity. We give numerical results for the frequencies of these new modes as function of temperature in an isotropic trap at unitarity.