Dynamics of discrete nonlinear schrodinger system for dipolar Bose-Einstein condensates in binary optical lattices

Abstract

In this research, the dynamical stability of coupled nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattices is investigated. Analytical and numerical studies have been conducted to check the dynamical stability of the system. The analytical study is carried out using strongly localized field modes approximation and subsequently, predicting the stability based on the system norm. On the other hand, there are two numerical approaches that are employed, namely, anti-continuum and modulational instability methods. However, the former considers only bulk-localized solution type and the latter presumes the solution in terms of plane wave profile. Nevertheless, for bulk-localized solution, two types of coupled field profiles are considered; bright symmetry unstaggered on-site and bright symmetry unstaggered inter-site. Thorough analysis on the strongly localized modes leads into parametric restrictions for the bulk-localized solutions, and has become the guidelines in the anti-continuum method. Furthermore, transient solutions for the corresponding dynamical system also have been computed for both bulk-localized and plane wave schemes and the behaviours of the system are in good agreement with the linear stability analysis. Essentially, both bulk-localized and plane wave solutions exist in the system and the relation of the dipolar interaction compared to the combination of local coupling and the atomic scattering length mainly determines the stability in the bulk-localized solution while in the plane wave profile, the stability is also determined by the similar energy balance however the comparison now has the neighbour interaction additional to the dipolar quantity