A Quantum Degenerate Mixture of $^{87}$Rb and $^{133}$Cs

This thesis reports the formation of a dual-species Bose-Einstein condensate of Rb and Cs in the same trapping potential. Quantum degenerate mixtures exhibit rich physics inaccessible to single species experiments and provide an ideal starting point for the creation of ultracold dipolar molecules. These molecules offer a wealth of new research avenues including precision metrology, quantum simulation and computation. The experimental 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. Evaporative cooling in the dipole trap must compete against a high interspecies three-body inelastic collision rate . 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 leads to the creation of single-species Cs condensates of up to atoms. In addition this thesis reports the observation of an interspecies Feshbach resonance at 181.7(5)~G and the creation of a pure sample of Cs molecules via magneto-association on the 4(g)4 resonance at 19.8~G. These results represent important steps towards the creation of ultracold polar RbCs molecules.