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Frontiers in Optics

Reduced rate equation models for accurate SAS of 87Rb D2 line

Rajni Bala, Joyee Ghosh, Vivek Venkataraman, Quantum Photonics Lab

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We propose simplified reduced 5-level and 7-level rate equation models to calculate saturated absorption spectra of the Rb D2 line, and experimentally verify for transitions from upper and lower hyperfine ground state of 87Rb, respectively.
DOI
10.1364/fio.2022.jw4a.78

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We present a theoretical and experimental study of polarization spectroscopy of rubidium atoms. All of the populations of the magnetic sublevels were calculated from the rate equations and used in the calculation of the polarization spectroscopy spectra. Using this model, we could generate theoretical line shapes of the polarization spectra on the D2{D}_{2}D2​ transitions of rubidium atoms. The experimental results demonstrated that our model accurately reproduced spectra for all transitions in hyperfine structures.
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 An experiment on the saturated absorption spectroscopy (SAS) of 87Rb-D2 line is performed using the Laguerre–Gaussian (LG) beam as structured light. The theoretical simulation of which is done by considering a four-level atom-laser coupled system. The theoretically simulated spectra fairly match with the experimentally observed spectra. The line-width narrowing behavior of both the observed hyperfine and crossover resonances in the Doppler-broadened probe absorption spectra is attributed by the spatially dependent Rabi frequency of the pump LG beam irrespective of the characteristics of the probe beam. The results also illustrated that the narrowing behavior of the line shapes of the hyperfine structure using the LG beam is universal in nature, i.e. irrespective of hyperfine or crossover transitions. This structured light-induced narrowing of line-width of the sub-Doppler hyperfine and crossover resonances can be utilized for high-precision laser frequency locking at a particular hyperfine or crossover transition. Moreover, a significant narrowing of hyperfine and crossover resonances with the variation of the orbital angular momentum (OAM) number of the LG beam shows that the generated SAS signal can be manipulated by using the OAM of the structured light as a control knob.