Formation of Faraday patterns in cigar-shaped Bose-Einstein condensates
The radial trap frequency of an elongated harmonic trap containing a Bose-Einstein condensate is modulated. The free evolution of the condensate fraction is studied using phase-contrast imaging, revealing the dynamics of a single sample over a period of time. Multiple measurement series are combined to study the long-term behavior of samples created under similar experimental conditions. A high-order axial mode, the Faraday pattern, is observed. A simple parametric oscillator model is presented to describe the formation of this axial mode. This model suggests the radial quadrupole mode couples into the high-order axial mode through a parametric resonance. Also, the Faraday pattern is used to determine the speed of sound in the condensate as a function of density. The determined speed of sound deviates up to 20% from the Bogoliubov speed of sound for found densities.