Faraday and Resonant Waves in Dipolar Cigar-Shaped Bose-Einstein Condensates

TL;DR

This paper investigates Faraday and resonant density waves in dipolar Bose-Einstein condensates, deriving analytical expressions and validating them through numerical simulations, highlighting the role of anisotropic dipole-dipole interactions.

Contribution

It introduces a variational approach to analyze driven dipolar condensates and provides analytical formulas for density wave periods considering anisotropic interactions.

Findings

Analytical expressions for density wave periods derived.

Good agreement between variational and numerical results.

Anisotropy of dipole interactions influences wave formation.

Abstract

Faraday and resonant density waves emerge in Bose-Einstein condensates as a result of harmonic driving of the system. They represent nonlinear excitations and are generated due to the interaction-induced coupling of collective oscillation modes and the existence of parametric resonances. Using a mean-field variational and a full numerical approach, we studied density waves in dipolar condensates at zero temperature, where breaking of the symmetry due to anisotropy of the dipole-dipole interaction (DDI) plays an important role. We derived variational equations of motion for the dynamics of a driven dipolar system and identify the most unstable modes that correspond to the Faraday and resonant waves. Based on this, we derived the analytical expressions for spatial periods of both types of density waves as functions of the contact and the DDI strength. We compared the obtained variational results with the results of extensive numerical simulations that solve the dipolar Gross-Pitaevskii equation in 3D, and found a very good agreement.