Quantum jumps in atomic systems

Abstract

We consider a three-level atomic system driven strongly on one transition and weakly on the other. The excited state on the weak transition is assumed to be metastable. We give an analysis of the fluorescence from the strong transition in terms of the elementary probability density ${p}_{[0}$,t)(${\mathrm{t}}_{1}$,${t}_{2}$,..., ${t}_{n}$) which gives us the probability density that exactly n photons are emitted at times ${t}_{1}$,${t}_{2}$,...,${t}_{n}$ by the atom in the time interval [0,t). We show that ${p}_{[0}$,t) essentially factorizes into products of conditional densities c\ifmmode \tilde{}\else \~{}\fi{}(\ensuremath{\tau}) that, given a photon is emitted at time zero, the next photon emission occurs at time \ensuremath{\tau}. This enables a simulation of the individual photon emissions to be given which shows directly the existence of prolonged dark windows in the fluorescence corresponding to the shelving of the electron in the metastable state or ``quantum jumps.''