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Journal of Physics Conference Series

On the efficiency of laser pumping of hyperfine structure sublevels of Rubidium-87 and Cesium-133 atoms

A. I. Magunov, Vitalii G Pal'chikov

Published Sep 1, 2021• 0 citations
Publisher

Abstract

The evolution of the hyperfine structure magnetic sublevel populations of 87 Rb and 133 Cs atoms in resonant linearly polarized laser fields is theoretically analyzed. Analytical expressions are obtained for stationary populations of the magnetic sublevels of the ground state 5 2 S 1/2 F g = 1, F f = 2 in 87 Rb and 6 2 S 1/2 F g = 3, F f = 4 in 133 Cs under optical pumping at the F g ↔ F e = F g and F f ↔ F e = F f transitions of the D 2 lines ( n 2 S 1/2 n 2 P 3/2 ) versus the initial populations. The characteristic population stabilization time are obtained by numerical solution for the density matrix equations, depending on the intensity of the laser fields and the detuning of the optical resonance. It is shown that the alternation of the polarization direction of the laser field at the transition F f ↔ F e = F f almost completely transfers atoms to the lower sublevel of the "clock" M1 transition F g M = 0 ↔ F f M = 0 in rubidium and cesium frequency standards, which proportionally increases the signal of the recording system.

DOI
10.1088/1742-6596/2036/1/012003

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The evolution of the hyperfine structure magnetic sublevel populations of 87 Rb and 133 Cs atoms in resonant linearly polarized laser fields is theoretically analyzed. Analytical expressions are obtained for stationary populations of the magnetic sublevels of the ground state 5 2 S 1/2 F g = 1, F f = 2 in 87 Rb and 6 2 S 1/2 F g = 3, F f = 4 in 133 Cs under optical pumping at the F g ↔ F e = F g and F f ↔ F e = F f transitions of the D 2 lines ( n 2 S 1/2 n 2 P 3/2 ) versus the initial populations. The characteristic population stabilization time are obtained by numerical solution for the density matrix equations, depending on the intensity of the laser fields and the detuning of the optical resonance. It is shown that the alternation of the polarization direction of the laser field at the transition F f ↔ F e = F f almost completely transfers atoms to the lower sublevel of the "clock" M1 transition F g M = 0 ↔ F f M = 0 in rubidium and cesium frequency standards, which proportionally increases the signal of the recording system.
The evolution of the populations of the magnetic sublevels of the cesium atom (133Cs isotope) in resonant laser fields with linear polarization is analyzed using the equations for the density matrix. Analytic expressions are derived for stationary populations resulting from laser-induced optical transitions on the hyperfine structure components F g = 3 ↔ F e = 2, 3 and F f = 4 ↔ F e = 3, 4 of lines D1 (62S1/2 → 62P1/2) and D2 (62S1/2 → 62P3/2) depending on the initial values of the populations. The numerical solution of the evolution equations gives the characteristic times of stabilization of the steady regime as functions of laser field intensities and detuning from optical resonance. We determine the sequences of optical transitions increasing (by more than an order of magnitude) the population of the lower sublevel 62S1/2F g = 3 M = 0 of the “clock” microwave transition F g = 3 M = 0 ↔ F f = 4 M = 0 in the cesium frequency standard, which increases the signal intensity in the recording system by the same proportion.
This paper reports an analytical calculation of the populations of the Zeeman sublevels of the cesium atom. We use a circularly polarized laser beam to pump the Cs-cell in the geomagnetic field. Using the approximate form of the optical Bloch equations, we obtain the time evolution functions of the populations of the Zeeman sublevels S1/2(F=4, mF=-4) and P1/2(F=4, mF=-3). The case of the laser detuning of δ=0, by increasing the pumping light intensity, we could enhance populations non-uniform distribution degree of the ground states and improve the pumping efficiency of the cesium atom. It is significant to enhance sensitivity and accuracy of the optically pumped magnetometer.
We present analytical solutions for the populations of the D 1 transition line of 85 Rb atoms. The time evolution of the populations of the magnetic sublevels in the excited state at the weak intensity limit exhibits several kinds of homogeneous or inhomogeneous second-order differential equations. General solutions of the differential equations result in an analytical form of the population in each magnetic sublevel as a function of the elapsed time, laser intensity, and laser frequency detuning.
In the Λ three-level system, we will make use of semi-classical density matrix method to analyze cesium (Cs) hyperfine structure of coherent population trapping (CPT) phenomenon. Coherent population trapping has been widely used in electromagnetically induced transparency, non-inversion laser, optical storage and ultra-slow speed of light fields, then strong-coupling light and weak detecting light form coherent laser light to change the hyperfine structure energy levels of particles number distribution, which impacts on laser pumping magnetic resonance. In this paper, we will discuss the theoretical analysis and system design of laser pumping cesium magnetometer, cesium atomic energy level formed hyperfine structure with the I-J coupling, the hyperfine structure has been further split into Zeeman sublevels for the effects of magnetic field. To use laser pump and RF magnetic field make electrons transition in the Zeeman sublevels to produce the results of magneto-optical double resonance and on this basis we analyze the influence of laser pumping magnetic resonance based on coherent population trapping.
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We investigate the population differences between ground-state hyperfine levels (5S1/2,F=2{5S}_{1/2},F=25S1/2​,F=2 and 5S1/2,{5S}_{1/2},5S1/2​, F=1F=1F=1) of an optically pumped 87Rb{}^{87}\mathrm{Rb}87Rb beam in a static magnetic field, taking into account the various kinds of atomic coherence (Zeeman, hyperfine, and optical). The pumping lasers are monochromatic and in resonance with the ${(5S}_{1/2},F=1\ensuremath{\leftrightarrow}{5P}_{1/2}{,F}^{\ensuremath{'}}=1)$ transition. By varying the polarization configuration of the pumping lasers, we find that the pumping efficiency is substantially enhanced when a $\ensuremath{\sigma}$-polarized laser and a $\ensuremath{\pi}$-polarized laser are counterpropagating. In this case, the pumping efficiency remains high even in a weak magnetic field, which explains qualitatively experimental data reported previously from a cesium beam experiment.