Faraday Waves and Collective Modes in Bose-Einstein Condensates

摘要

Using variational and perturbative methods we investigate the dynamics of a trapped Bose-Einstein condensate whose effective nonlinearity is harmonically modulated. We derive analytic formulae for the period of Faraday waves in low-and high-density, longitudinally-homogeneous condensates. Using the Poincare-Lindstedt analysis, we also analytically calculate frequency shifts of collective oscillation modes of spherically and axially-symmetric condensates due to the harmonic driving of the interaction.