Spatially chaotic distribution of atoms in Bose-Einstein condensate systems

In this paper, we study the spatially chaotic distribution of atoms in a Bose-Einstein condensate system, trapped in an asymmetric periodic potential. For a constant phase of condensate, without atom currents in the system, the space distributed structure of condensated atoms can be described by an undamped Duffing equation with double drivers. Through theoretical analyses, the Mel'nikov chaotic criterion for the system with a repulsive interatomic interaction is presented. Numerical simulations show that an increasing chemical potential can exert considerable suppression on the chaotic distribution of condensated atoms and even completely eliminate chaos. For a system with an attractive interatomic interaction, under some specific parametric conditions, adjusting the ratio between optical lattice potential amplitudes will force the condensated atoms from a periodic state into a spatially chaotic distribution; with the increase of chemical potential, the spatially chaotic distribution is completely suppressed.