Dynamics of a Bose-Einstein Condensate in Optical Trap

Dynamics of a 2D Bose-Einstein condensate in an optical trap is studied taking into consideration fluctuations of the far-off-resonance laser field intensity. The problem is described in the frame of the mean field Gross- Pitaevskii equation with randomly varying trap potential. An analytic approach based on the moments method has been employed to describe the noise induced evolution of the condensate properties. Stochastic parametric resonance in oscillations of the condensate width is proved to exist. For the condensate with negative scattering length, it is shown that the noise can delay or even prevent the collapse. Analytical predictions are confirmed by numerical simulations of the underlying PDE and ODE models.