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We report the formation of a dual-species Bose-Einstein condensate of Rb and Cs in the same trapping potential. Our method exploits the efficient sympathetic cooling of Cs via elastic collisions with Rb, initially in a magnetic quadrupole trap and subsequently in a levitated optical trap. The two condensates each contain up to atoms and exhibit a striking phase separation, revealing the mixture to be immiscible due to strong repulsive interspecies interactions. Sacrificing all the Rb during the cooling, we create single species Cs condensates of up to atoms.

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