Nonlinear dynamics of Bose-Einstein condensates

Azeddine Messikh, Bakhram Umarov

It is well known that the dynamics of the Bose Einstein condensate (BEC) trapped in an optical lattice can be described in tight-binding approximation by the discrete Nonlinear Schrodinger Equation (DNLSE) [1,2]. This model opens the way to study different aspects of the BEC dynamics in an optical lattice, such as discrete solitons and nonlinear localized modes and their stability and dynamics, modulational instability, superfluid-insulator transition, etc.

Yeong E. Kim, Alexander L. Zubarev

Benjamin Schlein

G. Wunner, H. Cartarius, T. Fabčič +5 more

The motto of this paper is: Let’s face Bose‐Einstein condensation through nonlinear dynamics. We do this by choosing variational forms of the condensate wave functions (of given symmetry classes), which convert the Bose‐Einstein condensates via the time‐dependent Gross‐Pitaevskii equation into Hamiltonian systems that can be studied using the methods of nonlinear dynamics. We consider in particular cold quantum gases where long‐range interactions between the neutral atoms are present, in addition to the conventional short‐range contact interaction, viz. gravity‐like interactions, and dipole‐dipole interactions. The results obtained serve as a useful guide in the search for nonlinear dynamics effects in numerically exact quantum calculations for Bose‐Einstein condensates. A main result is the prediction of the existence of stable islands as well as chaotic regions for excited states of dipolar condensates, which could be checked experimentally.

Paulsamy Muruganandam, Ramaswamy Radha

In chapter 9, the dynamics of collisionally inhomogenous Bose–Einstein condensates (BECs), focusing on Faraday and resonant waves in scalar and binary condensates is investigated. The dynamics of stable vortices arising out of spatially inhomogenous interactions in attractive BECs is analyzed. Further, the impact of cubic–quintic–septimal nonlinearities arising out of collisionally inhomogenous interactions on BECs is also examined.

Wu‐Ming Liu