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

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.

10 pages, 4 figures, minor changes in the text and additional reference added

References in corpus (10)

• Bose-Einstein condensation of chromium
• Observation of dipole-dipole interaction in a degenerate quantum gas
• Stabilizing a purely dipolar quantum gas against collapse
• Radial and angular rotons in trapped dipolar gases
• Exact hydrodynamics of a trapped dipolar Bose-Einstein condensate
• Exceptional Points in Atomic Spectra
• Structure formation during the collapse of a dipolar atomic Bose-Einstein condensate
• Ground-state structure and stability of dipolar condensates in anisotropic traps
• Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping
• Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction

Cited by in corpus (7)

• Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. II. Applications
• Collisions of anisotropic two-dimensional bright solitons in dipolar Bose-Einstein condensates
• Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept
• Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates
• Variational calculations on multilayer stacks of dipolar Bose-Einstein condensates
• Hyperchaos in a Bose-Hubbard chain with Rydberg-dressed interactions
• Verification of exceptional points in the collapse dynamics of Bose-Einstein condensates