Straightforward Measurement of Saturation Intensity of Doppler-Broadened Transitions: Application to Rubidium Vapour
Bibliographic record
Abstract
The commonly quoted saturation intensity of rubidium (Rb) for D2 transitions is 16.7 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{W}.\mathrm{m}^{-2}$</tex>. This value, however, is only accurate for the cycling transition, which renders the Rb atom to resemble a two-level system. In practice, the effective saturation intensity is influenced by various factors, such as the polarization of light, optical pumping, and atom collision which can redistribute the population. As a result, it is crucial to experimentally determine the effective saturation intensity. In this context, we demonstrate a novel yet simple experimental method to measure the effective saturation intensities of Doppler-broadened transitions in atomic vapours. Our method only requires on-resonance absorbance data for various input laser intensities, which can be obtained with a tunable CW laser without the need for precise frequency locking. We applied this method to measure the effective saturation intensities of all four Doppler-broadened D2 transitions in natural rubidium (Rb) vapour (27.8<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">%87</sup>Rb and 72.2 % <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${}^{\text{8}} {}^{\text{5}}Rb$</tex> ) at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r={35}^{\circ} \mathrm{C}$</tex>. The results show that the effective saturation intensities for Rb range from 0.752 to 16.8 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{W}.\mathrm{m}^{-2}$</tex>. Notably, for certain transitions (specifically, repump transitions), the effective saturation intensities were smaller than 16.7 W. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{m}^{-2}$</tex> (up to an order of magnitude), with potentially important implications for optical pumping in Doppler-broadened transitions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".