  We report the realization of a heteronuclear two-atom of $^{87}$Rb-$^{85}$Rb
in the ground state of an optical tweezer (OT). Starting by trapping two
different isotopic single atoms, a $^{87}$Rb and a $^{85}$Rb in two strongly
focused and linearly polarized OT with 4 $\mu$m apart, we perform
simultaneously three dimensional Raman sideband cooling for both atoms and the
obtained 3D ground state probabilities of $^{87}$Rb and $^{85}$Rb are 0.91(5)
and 0.91(10) respectively. There is no obvious crosstalk observed during the
cooling process. We then merge them into one tweezer via a species-dependent
transport, where the species-dependent potentials are made by changing the
polarization of the OTs for each species from linear polarization to the
desired circular polarization. The measurable increment of vibrational quantum
due to merging is $0.013(1)$ for the axial dimension. This two-atom system can
be used to investigate cold collisional physics, to form quantum logic gates,
and to build a single heteronuclear molecule. It can also be scaled up to
few-atom regime and extended to other atomic species and molecules, and thus to
ultracold chemistry.
