First and second sound of a unitary Fermi gas in highly elongated harmonic traps

TL;DR

This paper presents a theoretical analysis of first and second sound modes in a highly elongated unitary Fermi gas, showing their potential for experimental measurement and superfluid density determination.

Contribution

It provides full solutions to the one-dimensional two-fluid hydrodynamic equations for a unitary Fermi gas in elongated traps, linking mode frequencies to superfluid density and temperature.

Findings

Discretized mode frequencies depend on temperature and superfluid density.

Density fluctuations in second sound are measurable with current experiments.

Second sound frequencies can help determine superfluid density accurately.

Abstract

Using a variational approach, we present the full solutions of the simplified one-dimensional two-fluid hydrodynamic equations for a unitary Fermi gas trapped in a highly elongated harmonic potential, which is recently derived by Stringari and co-workers {[}Phys. Rev. Lett. \textbf{105}, 150402 (2010){]}. We calculate the discretized mode frequencies of first and second sound along the weak axial trapping potential, as a function of temperature and the form of superfluid density. We show that the density fluctuations in second sound modes, due to their coupling to first sound modes, are large enough to be measured in current experimental setups such as that exploited by Tey \textit{et al}. at the University of Innsbruck {[}Phys. Rev. Lett. \textbf{110}, 055303 (2013){]}. Owing to the sensitivity of second sounds on the form of superfluid density, the high precision of the measured second sound frequencies may provide us a promising way to accurately determine the superfluid density of a unitary Fermi gas, which so far remains elusive.