Faraday Patterns in low-dimensional Bose-Einstein Condensates

TL;DR

This paper demonstrates that Faraday patterns can be generated in low-dimensional Bose-Einstein condensates through trap modulation, revealing a threshold reduction near twice the trap frequency due to parametric excitation.

Contribution

It introduces a method to excite Faraday patterns in low-dimensional BECs via trap modulation and analyzes the threshold behavior related to internal mode excitation.

Findings

Faraday patterns can be excited by trap width modulation.

Pattern formation threshold decreases near twice the trap frequency.

Parametric excitation of internal breathing modes influences pattern emergence.

Abstract

We show that Faraday patterns can be excited in the weak confinement space of low-dimensional Bose-Einstein condensates by temporal modulation of the trap width, or equivalently of the trap frequency Omega_tight, in the tight confinement space. For slow modulation, as compared with Omega_tight, the low-dimensional dynamics of the condensate in the weak confinement space is described by a Gross-Pitaevskii equation with time modulated nonlinearity coefficient. For increasing modulation frequencies a noticeable reduction of the pattern formation threshold is observed close to 2*Omega_tight, which is related to the parametric excitation of the internal breathing mode in the tight confinement space. These predictions could be relevant for the experimental excitation of Faraday patterns in Bose-Einstein condensates.