Faraday patterns in low-dimensional Bose-Einstein condensates

Excitation of Faraday patterns in the weak confinement space of low-dimensional Bose-Einstein condensates (BEC) by a periodic modulation of the trap frequency, Ω_tight, in the tight confinement space is shown. For slow modulation the low-dimensional dynamics of the BEC 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 near 2Ω_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 BEC.