Localization of a two-component Bose–Einstein condensate in a two-dimensional bichromatic optical lattice

We consider a weakly interacting two-component Bose–Einstein condensate (BEC) in a two-dimensional (2D) quasi-periodic bichromatic optical lattice (BOL). The problem is studied by means of split-step Crank–Nicolson method. The effects of weak intra- and inter-component interactions on localization of a two-component BEC are investigated. It is shown that in the quasi-2D regime, due to the enhanced disorder, there is no symmetry breaking like that in the one-dimensional (1D) case under a sine-typed potential, while configurations of density profiles are also quite different from that in the 1D case. By modulating interactions, the interplay of disorder and weak repulsive or attractive interactions is studied in detail. The cases with sine- and cosine-typed potentials acting on components 1 and 2 respectively are also discussed.