Discrete chaotic states of a Bose-Einstein condensate

We find the different spatial chaos in a one-dimensional attractive Bose-Einstein condensate interacting with a Gaussian-like laser barrier and perturbed by a weak optical lattice. For the low laser barrier the chaotic regions of parameters are demonstrated and the chaotic and regular states are illustrated numerically. In the high barrier case, the bounded perturbed solutions which describe a set of discrete chaotic states are constructed for the discrete barrier heights and magic numbers of condensed atoms. The chaotic density profiles are exhibited numerically for the lowest quantum number, and the analytically bounded but numerically unbounded Gaussian-like configurations are confirmed. It is shown that the chaotic wave packets can be controlled experimentally by adjusting the laser barrier potential.