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Applied Optics

Error optimization in the detection of level crossing through the measurement of n^(2)(T)

J. J. Sanz, M. Á. Rebolledo

Published May 15, 1983• 8 citations
Publisher

Abstract

Equations for calculation of the crossing point determination error and the signal width error in level-crossing experiments are generalized when the normalized second-order factorial moment of the fluorescence obtained is measured. To minimize the magnitude of these errors we study the behavior of these values on varying the magnetic field sweep interval, the counting time, and the mean fluorescence intensity.

DOI
10.1364/ao.22.001555

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Physical Review A•Apr 1, 1984•14 citations
Equations for calculation of the crossing point determination error and the signal width error in level-crossing experiments are generalized when the normalized second-order factorial moment of the fluorescence obtained is measured. To minimize the magnitude of these errors we study the behavior of these values on varying the magnetic field sweep interval, the counting time, and the mean fluorescence intensity.
A level-crossing detection method is presented and developed based on measurement of the normalized second factorial moment n((2))(T) of the photon-counting distribution of the resultant fluorescence. Expression n((2))(T) is obtained, and the errors expected in the determination of signal width and crossing field are theoretically studied. The validity of the approximations performed to establish the theoretical model is proved by an experiment with a square-wave periodically modulated light beam.
In this paper we study the possibility of analyzing a low intensity light beam whose spectrum has two lines with Lorentzian or Gaussian profiles by measuring n(2)(T) (the normalized second-order factorial moment). To do this the spectrum is scanned periodically by a spectrometer, and the normalized second-order factorial moment of the beam intensity at the exit aperture of the spectrometer is measured. The errors involved in the determination of the width, relative height, and separation between the two lines are calculated and discussed.
The linewidth in level-crossing experiments as normally carried out is the sum of the natural widths of the levels concerned. We have reduced the linewidth by taking the fluorescent light, not from all atoms in the assembly, but from a sample biased in favour of those which have survived as excited atoms for times longer than the average. This was achieved by pulse techniques. Improved resolution was obtained of the components on the wing of the zero-field level-crossing curve for the level 3 2P3/2 in 23Na. The values obtained for the hyperfine-coupling constants are a = 185 ± 040 MHz, b = 30 ± 06 MHz, in agreement with values found in double-resonance experiments. The present values do not represent the limit of the method, since the experiment was designed to investigate the technique, not to make precision measurements. A theoretical analysis of the method reveals that level-crossing curves obtained by this technique may, in certain circumstances, have undesirable satellites. It is shown how the line profile may be controlled and improved without too great a sacrifice in statistical accuracy.
In this paper we present the values we obtained for the lifetime of the 52P125 ^{2}P_{\frac{1}{2}}52P21​​ level of 85Rb^{85}\mathrm{Rb}85Rb using the Hanle effect. These measurements were carried out using two different methods: through a multichannel signal analyzer by photon counting and through a new method based on the determination of the normalized second-order factorial moment n(2)(T){n}^{(2)}(T)n(2)(T) of the fluorescence obtained. We discuss the results and advantages of the new method.