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arXiv · 0711.0561

Variational theory of two-fluid hydrodynamic modes at unitarity

Edward Taylor·Hui Hu·Xia-Ji Liu·Allan Griffin
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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.

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Edward Taylor, Hui Hu, Xia-Ji Liu, Allan Griffin. 2007-11-05. Variational theory of two-fluid hydrodynamic modes at unitarity. https://doi.org/10.1103/physreva.77.033608

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