Roughness with a finite correlation length in a microtrap

We analyze the effects of roughness in the magnitude of the magnetic field produced by a current carrying microwire, which is caused by the geometric fluctuation of the edge of the wire. The relation between the fluctuation of the trapping potential and the height the atom trap lies above the wire is very well consistent with the experimental data when the colored noise with a finite correlation length is considered. On this basis, we generate the random potential and get the density distribution of the Bose-Einstein condensate (BEC) atoms by solving the Gross-Pitaevskii equation, which coincides well with the experimental image, especially in the number of fragmentations. The results help us further understand the nature of the fluctuation and predict its possible application in the precise measurement.