First and second sound in a dilute Bose gas across the BKT transition

TL;DR

This paper investigates the behavior of two distinct sound modes in a two-dimensional dilute Bose gas as it undergoes the BKT transition, revealing their velocities and characteristics through classical-field dynamics and experimental comparisons.

Contribution

It provides a detailed analysis of the two sound modes across the BKT transition, identifying their nature and velocity behavior using classical-field simulations aligned with recent experiments.

Findings

The non-Bogoliubov sound mode has a higher velocity than the Bogoliubov mode below the transition.

The sound modes exhibit weak temperature dependence across the BKT transition.

Driven responses show higher velocities for the B sound mode at high temperatures near the transition.

Abstract

We study the propagation of the two sound modes in two-dimensional Bose gases across the Berezinksii-Kosterlitz-Thouless (BKT) transition using classical-field dynamics, which is motivated by recent measurements of Christodoulou et al. Nature 594, 191 (2021). Based on the dynamic structure factor, we identify the two sound modes as the Bogoliubov (B) and the non-Bogoliubov (NB) sound mode below the transition, and as the diffusive and the normal sound mode above the transition. The NB sound mode velocity is higher than the B sound mode velocity, which we refer to as the weak-coupling regime of the sound modes. We excite the sound modes by driving the system as in the experiment and by perturbing the density with a step-pulse perturbation, as a secondary comparison. The driven response depends on the driving strength and results in higher velocities for the B sound mode at high temperatures near the transition, compared to the sound results of the dynamic structure factor and step-pulse excitation. We show that the higher mode velocity has a weak temperature dependence across the transition, which is consistent with the experimental observation.