Nonlinear Dynamics of Bose-Einstein Condensates with Long-Range Interactions

TL;DR

This paper explores the nonlinear dynamics of Bose-Einstein condensates with long-range interactions using variational methods, predicting stable and chaotic behaviors in excited states that can be experimentally tested.

Contribution

It introduces a Hamiltonian dynamical systems approach to Bose-Einstein condensates with long-range interactions, providing new insights into their nonlinear behavior.

Findings

Prediction of stable islands in dipolar condensates

Identification of chaotic regions for excited states

Guidance for experimental verification of nonlinear effects

Abstract

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.