  Light-induced nonlinear terms in the Gross-Pitaevskii equation arise from the
stimulated coherent exchange of photons between two atoms. For atoms in an
optical dipole trap this effect depends on the spatial profile of the trapping
laser beam. Two different laser beams can induce the same trapping potential
but very different nonlinearities. We propose a scheme to measure light-induced
nonlinearities which is based on this observation.
