Dispersive Propagation of Ultras low Pulses in an Atomic Bose-Einstein Condensate

One-dimensional propagation of ultraslow optical pulses in an atomic Bose-Einstein condensate taking into account the dispersion and the spatial inhomogeneity is investigated. Analytical and semi-analytical solutions of the dispersive inhomogeneous wave equation modeling the ultraslow pulse propagation are developed and compared against the standard wave equation solvers based upon Cranck-Nicholson and pseudo-spectral methods. The role of curvature of the trapping potential of the condensate on the amount of dispersion of the ultraslow pulse is pointed out.