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

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.

9 pages, 8 figures, published version in PRA

References in corpus (12)

• Precision Measurements of Collective Oscillations in the BEC-BCS Crossover
• Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
• Virial expansion for a strongly correlated Fermi gas
• Collective modes and ballistic expansion of a Fermi gas in the BCS-BEC crossover
• Collective Modes in a Unitary Fermi Gas across the Superfluid Phase Transition
• Comparative study of strong coupling theories of a trapped Fermi gas at unitarity
• Temperature of a trapped unitary Fermi gas at finite entropy
• First and second sound in a strongly interacting Fermi gas
• Variational theory of two-fluid hydrodynamic modes at unitarity
• First and second sound in cylindrically trapped gases
• Low-temperature thermodynamics of the unitary Fermi gas: superfluid fraction, first sound and second sound
• Scaling solutions of the two fluid hydrodynamic equations in a harmonically trapped gas at unitarity

Cited by in corpus (1)

• Second sound with ultracold atoms: A brief historical account