Scientific Report - BEC

Nonlinear dynamics and solitons 40Figure 1: Solitonic solution of the KP equation for a 2D condensate.the lifetime of the bound (resonant) states associated with their decay into Bogoliubovsound modes. Our analysis suggests that the bound states of the 2D soliton have a finitelifetime. Our results can be of interest for the investigation of ultracold bosonic gasesin disk-shaped confining potentials, where vortex pairs are known to play a crucial role[6]. The observation of solitons in these systems would represent a nice manifestationof nonlinear dynamics in low dimensional superfluids.Flow of a Bose-Einstein Condensate Past an ObstacleThe ˘Cerenkov effect was first discovered in the electromagnetic radiation emitted bycharged particles traveling through a dielectric medium at a speed larger than themedium’s phase velocity. The concept of ˘Cerenkov radiation can be generalized to anysystem where a source is uniformly moving through a homogeneous medium at a speedlarger than the phase velocity of some elementary excitation to which the source couples.In [7] we studied the density modulation that appears in a Bose-Einstein condensateflowing with supersonic velocity against an obstacle. We compared our theoreticalresults of the density perturbation induced in a Bose-Einstein condensate (BEC) whichflows against a localized obstacle at rest with the experimental images taken by theJILA group [8]. Modulo a Galilean transformation, the physics of a moving source ina stationary medium is in fact equivalent to the one of a uniformly moving mediuminteracting with a stationary defect. The experiment has been performed by letting aBEC expand at hypersonic speed against the localized optical potential of a far-detunedlaser beam. The observed density profiles are successfully reproduced by numerically