Spatial Chaos of Bose–Einstein Condensates in a Cigar-Shaped Trap

Abstract

The spatial chaos of Bose–Einstein condensates in a cigar-shaped trap is studied. For a system with a steady current, we construct the general solution of the 1st-order equation. From the boundedness condition of the general solution, we obtain the Melnikov function predicting the onset of chaos. The unpredictability of the system's distribution of atom density is also theoretically analyzed. For a 23Na system meeting the perturbation condition, numerical simulations show the existence of chaos, which is in accordance with our analytical results. Numerical simulations of a 87Rb system dissatisfying the perturbation condition also demonstrate that there exists chaos in the system. The case without a current is also investigated.