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arXiv:1207.1058

Counting Photons in the Lambda-Experiment

Anita Magdalena Dąbrowska

Published Jul 4, 2012• 0 citations
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Abstract

Dehmelt's Lambda-experiment for a three-level atom with simultaneously driven strong and weak transition is studied within quantum stochastic calculus approach. The statistics of the emitted photons is found by the method of generating functional of the corresponding two dimensional output counting process. In particular, the average waiting times for a count are calculated.

DOI
10.48550/arxiv.1207.1058

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Dehmelt's Lambda-experiment for a three-level atom with simultaneously driven strong and weak transition is studied within quantum stochastic calculus approach. The statistics of the emitted photons is found by the method of generating functional of the corresponding two dimensional output counting process. In particular, the average waiting times for a count are calculated.
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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.
We calculate from the quantum regression theorem the entire photon-counting statistics for the fluorescence from a laser-driven two-level system weakly coupled to a metastable third level, and compare the result with the statistics of a dichotomic Markov process. The comparison shows, that at least in the limit of an infinite intensity of the laser in a single experiment the sequence of photon counts should display randomly alternating periods with no counts and a nonzero counting rate as if the atom executed ``quantum jumps'' to and from the metastable state.
The physical parameters governing the dynamics of a light-emitting quantum system can be estimated from the photon counting signal. The information available in the full detection record can be analyzed by means of the distribution of waiting times between detection events. Our theory allows calculation of the asymptotic, long-time behavior of the sensitivity limit, and it applies to emission processes with branching towards different final states accompanied by the emission of distinguishable photons. We illustrate the theory by application to a laser-driven $\ensuremath{\Lambda}$-type atom.