Faraday Patterns in a Stack of Driven Quasi-One-Dimensional Dipolar Bose-Einstein Condensates

Abstract

In this thesis, we study pattern formation in a stack of periodically driven quasi one-dimensional dipolar Bose-Einstein condensates. We study the excitation spectrum of the spatially separated dipolar condensates using Bogoliubov theory. The excitations are collective in nature due to the long-range nature of the dipole-dipole interaction. The parametric modulation of the s-wave scattering length leads to density modulations whose dynamics depends on the lowest Bogoliubov mode. The nature of the Bogoliubov modes depends on the orientation of the dipoles. When the dipoles are aligned such that the inter-tube dipolar interactions are attractive, the lowest mode corresponds to in-phase density modulations, leading to transient stripe patterns. In contrast, when the inter-tube interactions are repulsive, the lowest mode has out-of-phase character, resulting in checkerboard patterns. We also study the dynamics of quenching the dipole angle up on initial pattern formation and observe that it leads to a dynamical transition between the patterns.