Bifurcations, order, and chaos in the Bose-Einstein condensation of dipolar gases

TL;DR

This paper investigates the stability, bifurcations, and chaotic dynamics of dipolar Bose-Einstein condensates using a variational approach to solve the Gross-Pitaevskii equation, revealing thresholds for collapse and complex motion patterns.

Contribution

It introduces a detailed analysis of bifurcation points and chaos in dipolar BECs, linking stability thresholds to exceptional points and exploring the dynamics of excited states.

Findings

Universal stability thresholds correspond to bifurcation points.

Existence of regular and chaotic oscillations in condensate dynamics.

Stable regions persist above the saddle point energy.

Abstract

We apply a variational technique to solve the time-dependent Gross-Pitaevskii equation for Bose-Einstein condensates in which an additional dipole-dipole interaction between the atoms is present with the goal of modelling the dynamics of such condensates. We show that universal stability thresholds for the collapse of the condensates correspond to bifurcation points where always two stationary solutions of the Gross-Pitaevskii equation disappear in a tangent bifurcation, one dynamically stable and the other unstable. We point out that the thresholds also correspond to "exceptional points," i.e. branching singularities of the Hamiltonian. We analyse the dynamics of excited condensate wave functions via Poincare surfaces of section for the condensate parameters and find both regular and chaotic motion, corresponding to (quasi-) periodically oscillating and irregularly fluctuating condensates, respectively. Stable islands are found to persist up to energies well above the saddle point of the mean-field energy, alongside with collapsing modes. The results are applicable when the shape of the condensate is axisymmetric.