A variational approach to Bogoliubov excitations and dynamics of dipolar Bose-Einstein condensates

Abstract

We investigate the stability properties and the dynamics of Bose-Einstein condensates with axial symmetry, especially with dipolar long-range interaction, using both simulations on grids and variational calculations. We present an extended variational ansatz which is applicable for axial symmetry and show that this ansatz can reproduce the lowest eigenfrequencies of the Bogoliubov spectrum, and also the corresponding eigenfunctions. Our variational ansatz is capable of describing the roton instability of pancake-shaped dipolar condensates for arbitrary angular momenta. After investigating the linear regime we apply the ansatz to determine the dynamics and show how the angular collapse is correctly described within the variational framework.

27 pages, 11 figures

References in corpus (13)

• Bose-Einstein condensation of chromium
• Observation of dipole-dipole interaction in a degenerate quantum gas
• Stabilizing a purely dipolar quantum gas against collapse
• d-wave collapse and explosion of a dipolar Bose-Einstein condensate
• Finite Temperature Models of Bose-Einstein Condensation
• Radial and angular rotons in trapped dipolar gases
• Bogoliubov modes of a dipolar condensate in a cylindrical trap
• Ground-state structure and stability of dipolar condensates in anisotropic traps
• Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. II. Applications
• Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept
• Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction
• Relation between the eigenfrequencies of Bogoliubov excitations of Bose-Einstein condensates and the eigenvalues of the Jacobian in a time-dependent variational approach
• Variational calculations on multilayer stacks of dipolar Bose-Einstein condensates