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arXiv:2010.15724 · Physical Review A

Collisionless sound of bosonic superfluids in lower dimensions

Luca Salasnich, F. Sattin

Published Apr 19, 2021• 1 citation
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Abstract

The superfluidity of low-temperature bosons is well established in the collisional regime. In the collisionless regime, however, the presence of superfluidity is not yet fully clarified, in particular in lower spatial dimensions. Here, we compare the Vlasov-Landau equation, which does not take into account the superfluid nature of the bosonic system, with the Andreev-Khalatnikov equations, which instead explicitly contain a superfluid velocity. We show that recent experimental data of the sound mode in a two-dimensional collisionless Bose gas of $^{87}\mathrm{Rb}$ atoms are in good agreement with both theories, but the sound damping is better reproduced by the Andreev-Khalatnikov equations below the Berezinskii-Kosterlitz-Thouless critical temperature ${T}_{c}$, while above ${T}_{c}$ the Vlasov-Landau results are closer to the experimental ones. For one-dimensional bosonic fluids, where experimental data are not yet available, we find larger differences between the sound velocities predicted by the two transport theories and, also in this case, the existence of a superfluid velocity reduces the sound damping.

DOI
10.1103/physreva.103.043324

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We theoretically investigate sound modes in a weakly-interacting collisional Bose gas in DDD dimensions. Using the Landau's two-fluid hydrodynamics and working within the Bogoliubov theory, we observe the hybridization of the first and second sound modes for D≥2D\ge 2D≥2. To model the recent measurements of the sound velocities in 2D, obtained around the Berezinskii-Kosterlitz-Thouless transition temperature and outside the very weakly-interacting regime, we derive a refined calculation of the superfluid density, finding a fair agreement with the experiment. In the 1D case, for which experimental results are currently unavailable, we find no hybridization, triggering the necessity of future experimental investigations. Our analysis provides a systematic understanding of sound propagation in a collisional weakly-interacting Bose gas in DDD dimensions.
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Sound propagation is a macroscopic manifestation of the interplay between the equilibrium thermodynamics and the dynamical transport properties of fluids. Here, for a two-dimensional system of ultracold fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover, and we analyze the system response to an external perturbation. In the low-temperature regime we reproduce the recent measurements [Phys. Rev. Lett. 124, 240403 (2020)] of the first sound velocity, which, due to the decoupling of density and entropy fluctuations, is the sole mode excited by a density probe. Conversely, a heat perturbation excites only the second sound, which, being sensitive to the superfluid depletion, vanishes in the deep BCS regime and jumps discontinuously to zero at the Berezinskii-Kosterlitz-Thouless superfluid transition. A mixing between the modes occurs only in the finite-temperature BEC regime, where our theory converges to the purely bosonic results.