Relativistic causality and quantum-mechanical states in the Fermi problem Original Research Article

We discuss the validity of relativistic causality in the excitation exchange of a pair of atoms in vacuo. This is usually described as the Fermi problem. The atoms are modeled as two-level systems and their coupling with the electromagnetic field is taken in the multipolar scheme and in the electric dipole approximation. The atomic dynamics is determined by a solution of the Heisenberg equations for the atomic pseudospin operators Sz, S+ and S−, which is valid for times smaller than the spontaneous decay time. We show that for each atom this dynamics is manifestly casual, because it is independent of the presence of the other atom for times up to t = Rc, where R is the interatomic distance. Since this treatment is only in terms of operators and does not make any reference to states, we conclude that causality is a fundamental feature of the Fermi problem which does not depend of the quantum-mechanical state of the atom-field system.