Causality in the excitation exchange between identical atoms

The interaction between two identical atoms, separated by a distance r that is large compared to an optical wavelength, is considered using an amplitude approach in the Schrodinger picture. When atom 1 is excited by a radiation pulse whose duration is long compared to an optical period but short compared to the time it takes for light to travel between the atoms, the probability for atom 2 to be excited is found to be identically zero for times t<r/c, provided only r-dependent terms in the probability are retained. The r-dependent probability amplitude for atom 2 to be excited and atom 1 to be in its ground state is not identically equal. to zero for t<r/c. Rather it oscillates at the natural frequency of the optical transition. The Schrodinger picture approach allows one to clearly identify the various terms that give rise to the excitation probabilities. A diagrammatic technique is developed that facilitates the calculation.