Introduction. History of ideas

In the same period, it was understood that the trapping of atoms by laser light might give birth to what is now called particle-trapping spectroscopy (Letokhov 19756). This would be an important supplement to the Doppler-free laser spectroscopy techniques developed earlier, namely standing-wave absorption saturation spectroscopy 

For example, at an intensity I of the counterpropagating traveling laser waves producing the standing laser wave of the order of (c/87t)Eo = 1 kWcm , and for a tjqjical atomic off-resonance polarizability x 10 cm , the condition (5.2) is satisfied only for atoms with quite a low temperature T 1 /itK. In the case of localization of atoms in a three-dimensional standing hght wave (an optical lattice) (Letokhov 1973c), the proportion of trapped atoms at normal temperature is very small. So, the 

Theoretical analysis of the simplest model of the interaction of a two-level atom (Fig. 2.4, for the case T2 = I/7) with counterpropagating laser beams has shown that laser cooling makes it possible to reach extremely low temperatures, five to six orders of magnitude lower than room temperatme. It has been shown that in a two-level atom model, the cooling mechanism is based on single-photon absorption (or emission) processes. The minimum temperatme of the atoms is reached at a red detuning equal to the natural half-width of the atomic transition line, that is, / =—7, and is determined by the natural half-width 7 of the atomic transition (Letokhov et al. 1976, 1977)  

The value of the temperature in eqn (5.3) is nowadays referred to as the Doppler temperature or Doppler cooling limit. At a typical value of the natural hnewidth of an allowed transition 2y = 27t X 10 MHz, the temperature To is of the order of 100 pK. Because of the great promise that laser cooling and subsequent laser trapping of atoms held for laser spectroscopy, researchers at the Institute of Spectroscopy in Troitsk, Russia, launched experiments in this field. By the time the first successful experiment was conducted (Andreyev et al. 1981, 1982), the first theoretical work, summarized in a review of the manipulation of atoms by the light pressure force of a resonant laser (Letokhov and Minogin 1981a), had already been completed. 

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