Faraday waves in Bose-Einstein condensates

TL;DR

This paper provides an analytical and numerical study of Faraday waves in Bose-Einstein condensates, explaining the resonance phenomena and matching experimental observations through a Mathieu-type analysis.

Contribution

It offers a fully analytical explanation of Faraday wave formation in BECs under periodic transverse confinement modulation, validated by numerical simulations and experimental data.

Findings

Analytical prediction of pattern periodicity matches experimental data

Good qualitative and quantitative agreement with experiments

Numerical simulations confirm theoretical results

Abstract

Motivated by recent experiments on Faraday waves in Bose-Einstein condensates we investigate both analytically and numerically the dynamics of cigar-shaped Bose-condensed gases subject to periodic modulation of the strength of the transverse confinement. We offer a fully analytical explanation of the observed parametric resonance, based on a Mathieu-type analysis of the non-polynomial Schr{\"o}dinger equation. The theoretical prediction for the pattern periodicity versus the driving frequency is directly compared with the experimental data, yielding good qualitative and quantitative agreement between the two. These results are corroborated by direct numerical simulations of both the one-dimensional non-polynomial Schr{\"o}dinger equation and of the fully three-dimensional Gross-Pitaevskii equation.