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Photon statistics of light resonantly scattered from a three-level atom

R. M. Evans

Published Jan 1, 1984• 0 citations
Publisher

Abstract

A laser spectroscopy system and the equipment needed for resonance-fluorescence studies with the photon-burst method in an extended interaction region were developed. To accommodate the long, variable transit times of thermal atoms across this extended region a resettable coincidence counter was used;The photon statistics of light scattered from the three-level 5535 A transition in barium were investigated. These statistics agreed well with theory developed in conjunction with this work. An atomic branching ratio of 375 (+OR-) 30 was obtained from the photon number distributions, establishing a new method for determining this quantity. The affect of radiation pressure upon the photon-burst lineshapes was observed. Because of the large number of photons scattered high sensitivity was obtained, allowing measurements with fluxes of less than one atom/sec. The results of this work are important for the study of the hyperfine structure of atoms with short-lived nuclei and in searches for long-lived but exotic nuclei.

DOI
10.31274/rtd-180813-6826

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A laser spectroscopy system and the equipment needed for resonance-fluorescence studies with the photon-burst method in an extended interaction region were developed. To accommodate the long, variable transit times of thermal atoms across this extended region a resettable coincidence counter was used;The photon statistics of light scattered from the three-level 5535 A transition in barium were investigated. These statistics agreed well with theory developed in conjunction with this work. An atomic branching ratio of 375 (+OR-) 30 was obtained from the photon number distributions, establishing a new method for determining this quantity. The affect of radiation pressure upon the photon-burst lineshapes was observed. Because of the large number of photons scattered high sensitivity was obtained, allowing measurements with fluxes of less than one atom/sec. The results of this work are important for the study of the hyperfine structure of atoms with short-lived nuclei and in searches for long-lived but exotic nuclei.
The sensitivity of high-resolution fluorescence spectroscopy has been enhanced by the detection of bursts of photons from single atoms crossing a laser beam. A tunable cw laser beam intersected a well-collimated atomic beam at right angles, and the fluorescent light was detected by an ellipsoidal collector and a photomultiplier. The passage of an atom through the beam was identified with a burst of detected photon pulses, which could be differentiated easily from the random background. For increasing burst multiplicity the spectra show improved background suppression and also significant peak narrowing. High-resolution spectra were obtained with as few as 10 atoms/sec crossing the laser beam. Statistical predictions for the case of transit-time limited signals are calculated and compared with results obtained for the Na 5890-\AA{} and Ba 5535-\AA{} transitions.
Abstract Resonance scattering techniques are very useful for high-resolution atomic spectroscopy. The applicability of these techniques has been much extended, particularly through the rapid development of tunable-laser technology. The use of a narrow-band tunable laser, acting on a collimated atomic beam, gives a direct method enabling, for example, hyperfine structure and isotope shift studies. The intensity of lasers allows stepwise excitations to be performed, and with the two-photon absorption technique, Doppler-free measurements on thermal gases are also possible. By using pulsed lasers, time-resolved measurements yielding radiative life-times and structural information can be performed. The basic resonance scattering methods can be combined with radiofrequency and coherence techniques to yield a resolution, limited only by the uncertainty relation. Optical double resonance and level-crossing techniques, not requiring a narrow-band light source, have been extensively used. Several examples of the application of resonance scattering methods are given.
Photon-correlation spectroscopy, using both time-interval distribution and burst multiplicity measurements, has been used to investigate the 460.7-nm resonance line of strontium in a low-density atomic beam. A model that considers transit times and thermal velocity distributions for the interval measurements is presented and compared with experimental results. The measurements can determine detection efficiency and absolute beam densities and evaluate nonstatistical behavior such as photomultiplier afterpulsing and dark-count correlation. Photon correlation provides substantial improvements in spectroscopic measurements: linewidths less than the natural lifetime limit are observed, and suppression of Lorentzian tails reduces isotopic interferences by several orders of magnitude. Signal-to-background noise ratios are also improved, with detection limits (1-sec integration) of 10 atoms per second.
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.
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 study the general properties of the photon statistics of fluorescence radiation, emitted by a two-level atom in a strong laser field and a perturber bath. We investigate the deviation of the factorial moments from a Poisson distribution, and we show that for long counting times the lowest-order correction can be expressed entirely by the quantity Q, which represents the deviation of the variance from the average. We introduce and evaluate the quantities gn(t), which serve as a measure for the deviation of the higher-order statistics from Poissonian statistics. Subsequently we obtain explicit expressions for the average waiting time for the appearance of the n th photon, after an arbitrary initialization of the counting process. It turns out that the average time delay is again determined by Q. Hence this parameter can be measured in a photon-counting experiment, which involves only the observation of a single photon, rather than an (in principle) infinite number of photons.