Resolving the puzzle of sound propagation in a dilute Bose-Einstein condensate

TL;DR

This paper introduces a unified wave model combining logarithmic and Gross-Pitaevskii nonlinearities to accurately describe sound propagation in dilute Bose-Einstein condensates, aligning well with experimental data and proposing new experimental constraints.

Contribution

It presents a novel unified model incorporating non-perturbative quantum vacuum effects into BEC wave dynamics, improving understanding of sound propagation.

Findings

Model agrees with sodium BEC sound data

Constraints placed on model parameters from experiments

Proposes experiment to measure characteristic density scale

Abstract

A unified model of a dilute Bose-Einstein condensate is proposed, combining of the logarithmic and Gross-Pitaevskii nonlinear terms in a wave equation, where the Gross-Pitaevskii term describes two-body interactions, as suggested by standard perturbation theory; while the logarithmic term is essentially non-perturbative, and takes into account quantum vacuum effects. The model is shown to have excellent agreement with sound propagation data in the condensate of cold sodium atoms known since the now classic works by Andrews and collaborators. The data also allowed us to place constraints on two of the unified model's parameters, which describe the strengths of the logarithmic and Gross-Pitaevskii terms. Additionally, we suggest an experiment constraining the value of the third parameter (the characteristic density scale of the logarithmic part of the model), using the conjectured attraction-repulsion transition of many-body interaction inside the condensate.