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

TL;DR

This paper theoretically studies first and second sound modes in a highly oblate trapped unitary Fermi gas, showing that second sound can be observed through density fluctuations and is sensitive to superfluid density.

Contribution

It introduces a simplified two-dimensional two-fluid hydrodynamic model for analyzing sound modes in a trapped unitary Fermi gas at finite temperatures.

Findings

Large coupling between first and second sound induces significant density fluctuations.

Second sound can be directly observed via in-situ density profile measurements.

Second sound breathing mode frequency is highly sensitive to superfluid density.

Abstract

We theoretically investigate first and second sound modes of a unitary Fermi gas trapped in a highly oblate harmonic trap at finite temperatures. Following the idea by Stringari and co-workers {[}Phys. Rev. Lett. \textbf{105}, 150402 (2010){]}, we argue that these modes can be described by the simplified two-dimensional two-fluid hydrodynamic equations. Two possible schemes - sound wave propagation and breathing mode excitation - are considered. We calculate the sound wave velocities and discretized sound mode frequencies, as a function of temperature. We find that in both schemes, the coupling between first and second sound modes is large enough to induce significant density fluctuations, suggesting that second sound can be directly observed by measuring \textit{in-situ} density profiles. The frequency of the second sound breathing mode is found to be highly sensitive to the superfluid density.