Collisionless sound of bosonic superfluids in lower dimensions

TL;DR

This paper compares two theoretical models for collisionless superfluid sound in low-dimensional bosonic systems, showing that superfluid effects influence sound damping and velocity, with experimental data supporting the models in 2D.

Contribution

It provides a detailed comparison of the Vlasov-Landau and Andreev-Khalatnikov equations for collisionless bosonic superfluids in lower dimensions, highlighting the role of superfluidity in sound propagation.

Findings

Experimental data in 2D agree with both models.

Superfluid velocity reduces sound damping.

Differences in predicted sound velocities are significant in 1D.

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 $^{87}$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.