We report an apparatus and method capable of producing Bose-Einstein condensates (BECs) of ~1x10^6 87Rb atoms, and ultimately designed for sympathetic cooling of 133Cs and the creation of ultracold RbCs molecules. The method combines several elements: i) the large recapture of a magnetic quadrupole trap from a magneto-optical trap, ii) efficient forced RF evaporation in such a magnetic trap, iii) the gain in phase-space density obtained when loading the magnetically trapped atoms into a far red-detuned optical dipole trap and iv) efficient evaporation to BEC within the dipole trap. We demonstrate that the system is capable of sympathetically cooling the |F=1,m_F=-1> and |1,0> sublevels with |1,+1> atoms. Finally we discuss the applicability of the method to sympathetic cooling of 133Cs with 87Rb.
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