We study from the point of view of quantum logic the properties of the collective oscillations of two Rydberg atoms in two harmonic traps. The difference in the frequency of two normal modes of motion expands with the difference in the mass of the two atoms. The probability of excitation of the motional quanta due to the strong dipole-dipole interaction can be made to be sufficiently small. Based on the normal modes of motion we present a scheme for quantum state transfer which is useful for quantum information process and for precision spectroscopy of atoms that lack suitable transitions for efficient laser cooling, internal state preparation, and detection.