Understanding the production of dual BEC with sympathetic cooling

We show, both experimentally and theoretically, that sympathetic cooling of $^{87}$Rb atoms in the $|F=2,m_F=2>$ state by evaporatively cooled atoms in the $|F=1,m_F=-1>$ state can be precisely controlled to produce dual or single condensate in either state. We also study the thermalization rate between two species. Our model renders a quantitative account of the observed role of the overlap between the two clouds and points out that sympathetic cooling becomes inefficient when the masses are very different. Our calculation also yields an analytical expression of the thermalization rate for a single species.