Propagation of First and Second Sound in a Highly-Elongated Trapped Bose Condensed Gas at Finite temperatures

TL;DR

This paper investigates the propagation of first and second sound in a highly-elongated trapped Bose-Einstein condensate at finite temperatures using an extended ZNG formalism, combining numerical simulations and analytical analysis.

Contribution

The study extends the ZNG formalism to highly-anisotropic traps and applies it to simulate and analyze sound propagation in Bose-condensed gases at finite temperatures.

Findings

Second sound dominates condensate motion at higher temperatures.

First sound contributes significantly in certain regimes.

Simulation results align with analytical hydrodynamic equations.

Abstract

We study sound propagation in Bose-condensed gases in a highly-elongated harmonic trap at finite temperatures. This problem is studied within the framework of Zaremba-Nikuni-Griffin (ZNG) formalism, which consistent of a generalized Gross-Pitaevskii (GP) equation for the condensate and the kinetic equation for a thermal cloud. We extend the ZNG formalism to deal with a highly-anisotropic trap potential, and use it to simulate sound propagation using the trap parameters corresponding to the experiment on sound pulse propagation at finite temperature. We focus on the high-density two-fluid hydrodynamic regime, and explore the possibility of observing first and second sound pulse propagation. The results of numerical simulation are compared with an analyitical results derived from linearized ZNG hydrodynamic equations. We show that the second sound mode makes a dominant contribution to condensate motion in relatively high temperature, while the first sound mode makes an appreciable contribution.