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Journal of Physics A Mathematical and General

On the photon statistics of the fluorescence radiation of a laser-driven single atom

Reinhard Reibold

Published Jan 7, 1993• 5 citations
Publisher

Abstract

The subject of the investigation are single atoms, for instance isolated in a Paul trap, which are driven by laser fields while their resonance radiation is measured by photon counters. For a rather wide class of experimental setups or theoretical models, a method is developed to determine the statistics of the photons observed. In contrast to other approaches it avoids referring to 'continuous measurements' or similar concepts, but tries to stay as far as possible within the framework of ordinary quantum mechanics. The method is illustrated by application to simple models.

DOI
10.1088/0305-4470/26/1/019

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The subject of the investigation are single atoms, for instance isolated in a Paul trap, which are driven by laser fields while their resonance radiation is measured by photon counters. For a rather wide class of experimental setups or theoretical models, a method is developed to determine the statistics of the photons observed. In contrast to other approaches it avoids referring to 'continuous measurements' or similar concepts, but tries to stay as far as possible within the framework of ordinary quantum mechanics. The method is illustrated by application to simple models.
Statistics of fluorescence photons emitted by a single two-level atom interacting with a continuous wave laser field are analyzed. The photon-counting distribution is calculated for the so-called intermediate fluorescence photons, i.e., those counted during the time interval between instants at which photons are emitted. The result is a sub-Poissonian (narrower than Poisson) distribution, which agrees with experimental observations. This intermediate-photon distribution is used to calculate the average number of fluorescence photons, the second factorial moment of the photon-counting distribution, and Mandel’s Q parameter commonly used to evaluate the deviation of photon statistics from the Poisson distribution. The theoretical expressions obtained for moments of the intermediate-photon distribution are different from well-known Mandel’s formulas.
Single molecule fluorescence experiments yield a stream of photocounts, whose statistical properties contain valuable information about processes within the molecule and in its microscopic environment. The photon statistics display features specific of single quantum systems and are therefore best discussed in the frame of a quantum mechanical theory of radiation. The present summary of a lecture given in April 2002 at the Hofgeismar Spring School on single molecules presents the main concepts used in quantum theory of light, together with a few useful references, and discusses some illustrations and applications to single molecule measurements drawn from the recent literature.
The photon counting statistics of the fluorescence of a single atom driven by a resonant coherent field has been calculated and the results checked experimentally. The authors examine the effect of detuning the coherent field and/or the effect of an additional thermal field on the photon counting statistics. They work with a master equation that they have used previously and derive exact results for the probability distribution function P(n, tau ) for the emitted photons and for the normalised second factorial moment Q. The subPoissonian character of the photon statistics, for which Q<0, is most pronounced for weak thermal fields or weak detuned coherent fields. For short counting times tau the statistic is dominated by any spontaneous emission that occurs, as expected. Increasing numbers of black-body photons tend to increase the Q values, as might be expected-especially in the case of an initially excited atom-but no simple rule emerges. The recent experiments in the microwave region on Rydberg atoms interacting with thermal radiation in (low-Q) cavities offers the possibility of observing thermal-field effects on the photon counting statistics.
In this contribution quantum-effects in the radiation-atom interaction will be reviewed. It is well known that most of the phenomena involving laser light can be described by semi-classical methods however phenomena such as laser noise the spectra and photon statistics of resonance fluorescence and the interaction of atoms in the single-atom maser require a quantization of the radiation field. In this paper we will describe results on the latter two effects. We will start with the discussion of resonance fluorescence. 1. RESONANCE FLUORESCENCE The resonant interaction of laser light with atomic systems has received considerable theoretical and experimental attention over the past decade. Until the advent of the laser light sources for spectroscopy consisted of ordinary spectral lamps excited by DC or RF discharges and produced light having a very broad spectral width and hence very short correlation time and a relatively low intensity. For such fields both the experimental and theoretical results are in general well understood. However the development of the laser made available light sources which are sufficiently intense that an atomic (or molecular) transition can be very easily saturated. In addition the lasers are highly monochromatic having a coherence time much greater than typical natural lifetimes of excited atomic states and finally tunable making it possible to selectively excite particular atomic transitions. The theoretical analysis of this physical situation requires the use of techniques more general than
We report measurements of an intensity-field correlation function of the resonance fluorescence of a single trapped 138Ba+ ion. Detection of a photon prepares the atom in its ground state, and we observe its subsequent evolution under interaction with a laser field of well-defined phase. We record the regression of the resonance fluorescence source field. This provides a direct measurement of the field of the radiating dipole of a single atom and exhibits its strong nonclassical behavior. In the setup, an interference measurement is conditioned on the detection of a fluorescence photon.