Entangling level-crossing interaction between independent atoms

Here, we are concerned with atomic separations smaller than the resonant wavelength and consider two nonidentical atoms interacting with a standing-wave laser field. We assume that one of the atoms is located at an antinode and the other is located at a node of the standing wave. In this case only the atom located at the antinode of the standing wave is driven by the laser field. Moreover, the dipole-dipole potential between the atoms, averaged over all possible orientations of the dipole moments in respect to the atomic axis, vanishes at this specific separation. This allows to manipulate the atoms even at such small separations.