Localization of a two-component Bose–Einstein condensate in a one-dimensional random potential

We consider a weakly interacting two-component Bose–Einstein condensate (BEC) in a one-dimensional random speckle potential. The problem is studied with solutions of Gross–Pitaevskii (GP) equations by means of numerical method in Crank–Nicolson scheme. Properties of various cases owing to the competition of disorder and repulsive interactions of a cigar-shaped two-component BEC are discussed in detail. It is shown that in the central region, phase separation of a two-component BEC is not only affected by the intra- and inter-component interactions, but also influenced by the strength of the random speckle potential. Due to the strong disorder of the potential, the criterion of phase separation which is independent of the trap strength in an ordered potential, such as a harmonic potential, is no longer available. The influence of different random numbers generated by distinct processes on localization of BEC in the random potential is also investigated, as well as the configurations of the density profiles in the tail regions.