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Journal of Physics B Atomic Molecular and Optical Physics

Electron shelving in a lattice system

Ilya Sh. Averbukh

Published Jun 28, 1990• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0953-4075/23/12/026

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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.
A quantum-statistical theory is developed for a single-atom, three-state quantum system where a strong (1-3) and a weak (2-3) transition are driven resonantly by an incoherent field. From a second-order correlation function of the fluorescence intensity, it is concluded that a quantum jump can occur, in the sense that the single atom can undergo large fluctuations between a state of full emission in the strong transition to a state of no emission when the electron is shelved in the metastable state (2).
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.
One of the experiments made possible by the trapping and cooling of a single atom is to observe the quantum jumps to a metastable state in the atom by monitoring the resonance fluorescence of a strong transition in which at least one of the states is coupled to the metastable state. When the atomic electron moves to the metastable state, the fluorescence from the strongly driven transition disappears. When the electron drops back into the strongly driven transition, the fluorescence abruptly returns. Statistical analysis of these random interruptions to the fluorescence signal implies photon antibunching in the emission of the weak photon.
One of the elementary processes in quantum magnetism is the propagation of spin excitations. Here we study the quantum dynamics of a deterministically created spin-impurity atom, as it propagates in a one-dimensional lattice system [1]. We probe the spatial probability distribution of the impurity at different times using single-site-resolved imaging of bosonic atoms in an optical lattice. In the Mott-insulating regime, the quantum-coherent propagation of a magnetic excitation in the Heisenberg model can be observed using a post-selection technique. Extending the study to the superfluid regime of the bath, we quantitatively determine how the bath affects the motion of the impurity, showing evidence of polaronic behaviour. The experimental data agree with theoretical predictions, allowing us to determine the effect of temperature on the impurity motion. Our results provide a new approach to studying quantum magnetism, mobile impurities in quantum fluids and polarons in lattice systems.
By means of a physically interesting example, it is shown how the mathematical theory of quantum stochastic calculus can be used in modelling physical systems. The example is the so-called electron shelving effect. The fluorescent light emitted by a single atom or ion presents periods of darkness if two transitions, one weak and one strong, are simultaneously driven. By a previously developed theory of counting processes, based on quantum stochastic differential equations, the full statistics of the emitted photons is obtained. In particular, the results on the duration of bright and dark periods, previously obtained by Cohen-Tannoudji and Dalibard (1986), are completely confirmed.