  We report the production of a high phase-space density mixture of $^{87}$Rb
and $^{133}$Cs atoms in a levitated crossed optical dipole trap as the first
step towards the creation of ultracold RbCs molecules via magneto-association.
We present a simple and robust experimental setup designed for the sympathetic
cooling of $^{133}$Cs via interspecies elastic collisions with $^{87}$Rb.
Working with the $|F=1, m_F=+1 >$ and the $|3, +3 >$ states of $^{87}$Rb and
$^{133}$Cs respectively, we measure a high interspecies three-body inelastic
collision rate $\sim 10^{-25}-10^{-26} \rm{cm}^{6}\rm{s}^{-1}$ which hinders
the sympathetic cooling. Nevertheless by careful tailoring of the evaporation
we can produce phase-space densities near quantum degeneracy for both species
simultaneously. In addition we report the observation of an interspecies
Feshbach resonance at 181.7(5) G and demonstrate the creation of Cs$_{2}$
molecules via magneto-association on the 4g(4) resonance at 19.8 G. These
results represent important steps towards the creation of ultracold RbCs
molecules in our apparatus.
