Interaction potential of two nonidentical ground-state atoms

We study the interaction potential of two nonidentical ground-state atoms coupled to a scalar field in a vacuum by separately calculating the contributions of vacuum fluctuations and those of the radiation reaction of the atoms. Both cases of atoms in a free space and in parallel or vertical alignment to a reflecting boundary are considered. For the former case, we find that the leading-order interaction potential in the region lambda(A) << L << lambda(B) exhibits the same separation-dependence as that in the region L << lambda(A) << lambda(B), where L, lambda(A) and lambda(B) are respectively the interatomic separation and the transition wavelengths of two atoms with lambda(A) << lambda(B). For the latter case, we find that boundary-induced modifications are very remarkable when L >> z, with z characterizing the separation between the two-atom system and the boundary. Particularly, when L further satisfies L >> lambda(A) and L >> lambda(B), the interaction potential in the parallel- and the vertical-alignment cases respectively scales as z(4)L(-7) and z(2)L(-5), the L-dependence of which is one order higher than those of two atoms in regions where L >> z and meanwhile L << lambda(A) or/and L << lambda(B). Our results suggest that retardation for the interaction potential of two nonidentical atoms with remarkably distinctive transition frequencies happens only when the interatomic separation is much greater than the transition wavelengths of both atoms.