Speed of sound in a Bose-Einstein condensate

TL;DR

This paper calculates the speed of sound in a Bose-Einstein condensate confined in a harmonic trap, analyzing its temperature dependence and comparing theoretical predictions with experimental data, including potential explanations for discrepancies.

Contribution

It provides a theoretical derivation of the speed of sound in a trapped Bose-Einstein condensate using an N-body Hamiltonian and explores the impact of temperature and formalism choices.

Findings

Derived an expression for the speed of sound as a function of temperature.

Compared theoretical predictions with experimental results for sodium condensates.

Discussed the potential of the Zaremba-Nikuni-Griffin formalism to resolve discrepancies.

Abstract

In the present work we determine the speed of sound in a Bose-Einstein condensate confined by an isotropic harmonic oscillator trap. The deduction of this physical parameter is done resorting to the $N$-body Hamiltonian operator. The single-particle eigenfunctions that have been employed in this formalism are those stemming from the corresponding harmonic oscillator potential, and an expression for the dependence of this speed on the temperature is also deduced. These functions are used in the calculation of the scaterring length, etc. The situation for a Bose-Einstein condensate of sodium is evaluated and the corresponding speed of sound is obtained and compared against the known experimental outcomes. The possibility that the solution, to the existing discrepancy between experiment and theoretical predictions, could be given by the Zaremba-Nikuni-Griffin formalism is also explored.