First and Second Sound Modes of a Bose-Einstein Condensate in a Harmonic Trap

TL;DR

This paper calculates the first and second sound modes of a dilute Bose-Einstein condensate in a spherical trap across various temperatures and particle numbers, revealing temperature-dependent behaviors and matching recent experimental observations.

Contribution

It provides detailed calculations of sound modes in Bose-Einstein condensates for a wide range of system sizes and temperatures, connecting theory with recent experimental findings.

Findings

Second sound modes are more temperature-sensitive than first sound modes.

Temperature variations near T_c match experimental data from JILA.

Sound mode behaviors are consistent across different system sizes.

Abstract

We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures ($0.6<T/T_{c}<1.2$) and for systems with $10^4$ to $10^8$ particles. The second sound modes (which exist only below $T_{c}$) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near $T_{c}$ recently observed at JILA in systems with $10^3$ particles match surprisingly well with those of the first and second sound modes of much larger systems.