Competition between Zeeman and hyperfine pumping in thermal atomic vapor

Rajni Bala; Joyee Ghosh; Vivek Venkataraman; Vivek Venkataraman

doi:10.1364/JOSAB.498324

Journal of the Optical Society of America B
Vol. 40,
Issue 10,
pp. 2595-2603
(2023)
•https://doi.org/10.1364/JOSAB.498324

Competition between Zeeman and hyperfine pumping in thermal atomic vapor

Rajni Bala, Joyee Ghosh, and Vivek Venkataraman

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Rajni Bala, Joyee Ghosh, and Vivek Venkataraman, "Competition between Zeeman and hyperfine pumping in thermal atomic vapor," J. Opt. Soc. Am. B 40, 2595-2603 (2023)

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Abstract

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 ${^{87}{\rm Rb}}$ ${{\rm D}_2}$ line (residual error ${\lt}\;{2}\%$) without any fitting parameters, while being ${\sim}100 \times$ 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.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (31)

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Upper		Lower
$C_{2, 0}^{2}$	0	$C_{1, 0}^{2}$	1/9
$C_{2, 1}^{2}$	1/18	$C_{1, 1}^{2}$	5/18
$C_{2, 2}^{2}$	5/18	$C_{1, 2}^{2}$	5/18
$C_{2, 3}^{2}$	7/9	$C_{1, 3}^{2}$	0

(a) $S_{F_{g}, m_{i} \to F_{e}, m_{i} + 1}$ in multiple of “sp” for $σ^{+}$ transitions
$m_{i}$	$Δ F = - 1$	$Δ F = 0$	$Δ F = 1$
$m_{a}$	$S_{2, 0 \to 1, 1} = \frac{1}{10}$	$S_{2, - 1 \to 2, 0} = \frac{3}{10}$	$S_{2, - 1 \to 3, 0} = \frac{3}{35}$
		$S_{2, 0 \to 2, 1} = \frac{3}{10}$	$S_{2, 0 \to 3, 1} = \frac{6}{35}$
		$S_{2, 1 \to 2, 2} = \frac{2}{10}$	$S_{2, 1 \to 3, 2} = \frac{10}{35}$
$m_{a_{p}^{'}}$	$S_{2, 1 \to 1, 2} = 0$	$S_{2, 2 \to 2, 3} = 0$	$S_{2, 2 \to 3, 3} = \frac{15}{35}$
	$S_{2, 2 \to 1, 3} = 0$
$m_{a_{m}^{'}}$	$S_{2, - 1 \to 1, 0} = \frac{3}{10}$	$S_{2, - 2 \to 2, - 1} = \frac{2}{10}$	$S_{2, - 2 \to 3, - 1} = \frac{6}{35}$
	$S_{2, - 2 \to 1, - 1} = \frac{6}{10}$
(b) $S_{F_{g}, m_{i} \to F_{e}, m_{i} - 1}$ in multiple of “sm” for $σ^{-}$ transitions
$m_{i}$	$Δ F = - 1$	$Δ F = 0$	$Δ F = 1$
$m_{a}$	$S_{2, 0 \to 1, - 1} = \frac{1}{10}$	$S_{2, - 1 \to 2, - 2} = \frac{2}{10}$	$S_{2, - 1 \to 3, - 2} = \frac{10}{35}$
		$S_{2, 0 \to 2, - 1} = \frac{3}{10}$	$S_{2, 0 \to 3, - 1} = \frac{6}{35}$
		$S_{2, 1 \to 2, 0} = \frac{3}{10}$	$S_{2, 1 \to 3, 0} = \frac{3}{35}$
$m_{a_{p}^{'}}$	$S_{2, 1 \to 1, 0} = \frac{3}{10}$	$S_{2, 2 \to 2, 1} = \frac{2}{10}$	$S_{2, 2 \to 3, 3} = \frac{1}{35}$
	$S_{2, 2 \to 1, 1} = \frac{6}{10}$
$m_{a_{m}^{'}}$	$S_{2, - 1 \to 1, - 2} = 0$	$S_{2, - 2 \to 2, - 3} = 0$	$S_{2, - 2 \to 3, - 3} = \frac{15}{35}$
	$S_{2, - 2 \to 1, - 3} = 0$

Upper		Lower
$C_{2, 0}^{2}$	0	$C_{1, 0}^{2}$	1/9
$C_{2, 1}^{2}$	1/18	$C_{1, 1}^{2}$	5/18
$C_{2, 2}^{2}$	5/18	$C_{1, 2}^{2}$	5/18
$C_{2, 3}^{2}$	7/9	$C_{1, 3}^{2}$	0

(a) $S_{F_{g}, m_{i} \to F_{e}, m_{i} + 1}$ in multiple of “sp” for $σ^{+}$ transitions
$m_{i}$	$Δ F = - 1$	$Δ F = 0$	$Δ F = 1$
$m_{a}$	$S_{2, 0 \to 1, 1} = \frac{1}{10}$	$S_{2, - 1 \to 2, 0} = \frac{3}{10}$	$S_{2, - 1 \to 3, 0} = \frac{3}{35}$
		$S_{2, 0 \to 2, 1} = \frac{3}{10}$	$S_{2, 0 \to 3, 1} = \frac{6}{35}$
		$S_{2, 1 \to 2, 2} = \frac{2}{10}$	$S_{2, 1 \to 3, 2} = \frac{10}{35}$
$m_{a_{p}^{'}}$	$S_{2, 1 \to 1, 2} = 0$	$S_{2, 2 \to 2, 3} = 0$	$S_{2, 2 \to 3, 3} = \frac{15}{35}$
	$S_{2, 2 \to 1, 3} = 0$
$m_{a_{m}^{'}}$	$S_{2, - 1 \to 1, 0} = \frac{3}{10}$	$S_{2, - 2 \to 2, - 1} = \frac{2}{10}$	$S_{2, - 2 \to 3, - 1} = \frac{6}{35}$
	$S_{2, - 2 \to 1, - 1} = \frac{6}{10}$
(b) $S_{F_{g}, m_{i} \to F_{e}, m_{i} - 1}$ in multiple of “sm” for $σ^{-}$ transitions
$m_{i}$	$Δ F = - 1$	$Δ F = 0$	$Δ F = 1$
$m_{a}$	$S_{2, 0 \to 1, - 1} = \frac{1}{10}$	$S_{2, - 1 \to 2, - 2} = \frac{2}{10}$	$S_{2, - 1 \to 3, - 2} = \frac{10}{35}$
		$S_{2, 0 \to 2, - 1} = \frac{3}{10}$	$S_{2, 0 \to 3, - 1} = \frac{6}{35}$
		$S_{2, 1 \to 2, 0} = \frac{3}{10}$	$S_{2, 1 \to 3, 0} = \frac{3}{35}$
$m_{a_{p}^{'}}$	$S_{2, 1 \to 1, 0} = \frac{3}{10}$	$S_{2, 2 \to 2, 1} = \frac{2}{10}$	$S_{2, 2 \to 3, 3} = \frac{1}{35}$
	$S_{2, 2 \to 1, 1} = \frac{6}{10}$
$m_{a_{m}^{'}}$	$S_{2, - 1 \to 1, - 2} = 0$	$S_{2, - 2 \to 2, - 3} = 0$	$S_{2, - 2 \to 3, - 3} = \frac{15}{35}$
	$S_{2, - 2 \to 1, - 3} = 0$

Abstract

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Equations (31)

Journal of the Optical Society of America B