Abstract We theoretically and experimentally investigate the Doppler-broadened absorption spectrum of the D2-line (52 S 1/2 → 52 P 3/2) in thermal (room-temperature) Rb vapour over a wide range of probe intensity, probe diameter, and vapour cell temperature to understand the effect of hyperfine pumping and transit-relaxation on the absorption lineshape. We present a relatively simple but comprehensive five-level rate equation model which incorporates optical pumping of the atomic population into the other ‘dark’ ground hyperfine level (leading to absorption saturation), including contributions of the three closely spaced (within one Doppler linewidth) hyperfine levels in the excited state 52 P 3/2 (allowed by the dipole transition selection rules). D2-line transmission spectra predicted by our model show excellent agreement (rms error < 5 % ) with the experimental data for a wide range of probe intensities (from ∼ 0.001 I s a t 0 all the way up to ∼ 10 I s a t 0 , where I sat0 is the usual two-level saturation intensity for the respective atomic transition), vapour cell temperatures (24.2°C–53.5 °C) and beam diameters (1/e 2 width ∼ 1 − 6 mm). Our model also takes into account the finite transit time of atoms across the probe beam cross-section, and correctly predicts the dependence of effective saturation intensity on probe diameter (up to ∼ 10 × lower saturation intensity as compared to I sat0 for few-mm beam sizes). This ab initio five-level model can thus predict accurate Doppler lineshapes for any given experimental parameter set for a linearly polarized probe without any fitting parameters, and can be easily applied to any other atomic system by an appropriate change of the atomic constants in the rate equations.
Abstract. We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2 % for the D2 line at 16.5 ◦ C. PACS numbers: 32.70.-n, 32.70.Fw, 42.62.FiAbsolute Rb absorption 2 1.
We present ab initio reduced rate equation models to study the interplay of Zeeman and hyperfine pumping, which determines the Doppler-broadened absorption spectra of an arbitrarily polarized probe laser, in thermal atomic vapor. Our simple models (with maximum seven levels) accurately predict the dependence of probe absorption on its polarization for the 87Rb D2 line (residual error <2%) without any fitting parameters, while being ∼100× less computational resource intensive as compared to numerically complex full multi-level models that treat all (up to 23) the magnetic (m F ) sub-levels present in the system individually. We demonstrate that either Zeeman or hyperfine pumping dominates depending on whether the atomic transitions being probed are primarily closed or open.
The commonly quoted saturation intensity of rubidium (Rb) for D2 transitions is 16.7
W.m−2. 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%87Rb and 72.2 %
85Rb) at
r=35∘C. The results show that the effective saturation intensities for Rb range from 0.752 to 16.8
W.m−2. Notably, for certain transitions (specifically, repump transitions), the effective saturation intensities were smaller than 16.7 W.
m−2(up to an order of magnitude), with potentially important implications for optical pumping in Doppler-broadened transitions.
We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2% for the D2 line at 16.5 degrees C.