It is shown that the 'electron shelving scheme' used in experiments on quantum jumps in single atoms may serve as an effective tool for investigation of electron dynamics in spatially distributed quantum systems. The statistics of long interruptions in resonance fluorescence of a single impurity incorporated into a model lattice system is considered. It is shown that the statistics reflects the character of the electron motion on the lattice in the vicinity of the impurity. Both the cases of coherent and incoherent electron dynamics are discussed.
The observation of quantum jumps in a Dehmelt electron-shelving scheme was made two years ago.1 Prior to these experiments considerable theoretical discussion was addressed to the question of whether the turn-on and turn-off of fluorescence, as described by Cook and Kimble,2 would actually occur. This discussion focused on photon statistics. It was taken to be self-evident that a prolonged cessation of fluorescence from the strong transition implied that the atom had jumped and now resided in the shelved state. This is surely correct but with some qualification. What observational information leads to the conclusion that the electron is shelved? It is the appearance of an abnormally long time interval without recording a single photoelectron at the detector monitoring the strong fluorescence. But how long is abnormally long? What is the time resolution of our quantum jump? I calculate the reduced atomic state following a photoelectric detection event, conditioned on the requirement that no subsequent photoelectron has been observed. For sufficiently long times without recording a subsequent photoelectron the atomic state collapses to the shelved state with high (but not unit) probability. The waiting time required for a confident judgment that the atom is in the shelved state is calculated as a function of transition rates and detector efficiency.