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 excit ed 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 bet ween the atoms, the probability for atom 2 to be excited is found to b e identically zero for times t<r/c, provided only r-dependent terms in the probability are retained. The r-dependent probability amplitude f or atom 2 to be excited and atom 1 to be in its ground state is not id entically equal. to zero for t<r/c. Rather it oscillates at the natura l frequency of the optical transition. The Schrodinger picture approac h allows one to clearly identify the various terms that give rise to t he excitation probabilities. A diagrammatic technique is developed tha t facilitates the calculation.