Dynamical Kosterlitz-Thouless Theory for Two-Dimensional Ultracold Atomic Gases

Abstract

In this letter we develop a theory for the first and second sound in a two-dimensional atomic superfluid across the superfluid transition based on the dynamic Koterlitz-Thouless theory. We employ a set of modified two-fluid hydrodynamic equations which incorporate the dynamics of the quantised vortices, rather than the conventional ones for a three-dimensional superfluid. As far as the sound dispersion equation is concerned, the modification is essentially equivalent to replacing the static superfluid density with a frequency dependent one, renormalised by the frequency dependent "dielectric constant" of the vortices. This theory has two direct consequences. First, because the renormalised superfluid density at finite frequencies does not display discontinuity across the superfluid transition, in contrast to the static superfluid density, the sound velocities vary smoothly across the transition. Second, the theory includes dissipation due to free vortices, and thus naturally describes the sound-to-diffusion crossover for the second sound in the normal phase. With only one fitting parameter, our theory gives a perfect agreement with the experimental measurements of sound velocities across the transition, as well as the quality factor in the vicinity of the transition. The predictions from this theory can be further verified by future experiments.

arXiv comment11 pages, 4 figures

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Cited by in corpus (6)

• Observation of first and second sound in a BKT superfluid
• Propagation of first and second sound in a two-dimensional Fermi superfluid
• Mutual friction and diffusion of two-dimensional quantum vortices
• First and second sound in a dilute Bose gas across the BKT transition
• Mechanism for sound dissipation in a two-dimensional degenerate Fermi gas
• Collisionless sound of bosonic superfluids in lower dimensions