Deviations from exponential decay in the case of spontaneous emission from a two-level atom

Abstract

A mathematically rigorous treatment of the Weisskopf-Wigner model of atomic spontaneous emission is presented. For the first time to the authors' knowledge, it is shown that in the correct asymptotic treatment with a cutoff frequency at which the dipole approximation breaks down, the main contribution to the long-time deviation from the exponential decay is of the order of 1/(t ${\mathrm{ln}}^{2}$t). This contradicts the results of previous authors who have obtained a long-time behavior of the order of 1/${t}^{2}$ by nonrigorous mathematical treatment of the same model in the dipole approximation. However, we will show that the result 1/${t}^{2}$ can still be obtained if the retardation effects are taken into account, i.e., if no dipole approximation is made.