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Journal of Experimental and Theoretical Physics

Selective laser pumping of magnetic sublevels in the hyperfine structure of the cesium atom

Alexandr I. Magunov, Vitalii G Pal'chikov

Published May 1, 2014• 3 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776114040141

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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.
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 D1 line spectrally selective pumping process in Doppler-broadened cesium is analyzed by solving the optical Bloch equations. The process, described by a three-level model with the Λ scheme, shows that the saturation intensity of broadened atoms is three orders of magnitude larger than that of resting atoms. The |Fg = 3〉 → |Fe = 4〉 resonance pumping can result in the ground state |Fg = 4, mF = 4〉 sublevel having a maximum population of 0.157 and the population difference would be about 0.01 in two adjacent magnetic sublevels of the hyperfine (HF) state Fg = 4. To enhance the anisotropy in the ground state, we suggest employing dichromatic optical HF pumping by adding a laser to excite D1 line |Fg = 4〉 → |Fe = 3〉 transition, in which the cesium magnetometer sensitivity increases by half a magnitude and is unaffected by the nonlinear Zeeman effect even in Earth's average magnetic field.
The D1 line spectrally selective pumping process in Doppler-broadened cesium is analyzed by solving the optical Bloch equations. The process, described by a three-level model with the A scheme, shows that the saturation intensity of broadened atoms is three orders of magnitude larger than that of resting atoms. The 丨Fg = 3） →丨Fe = 4） resonance pumping can result in the ground state丨Fg = 4, mF = 4） sublevel having a maximum population of 0.157 and the population difference would be about 0.01 in two adjacent magnetic sublevels of the hyperfine （HF） state Fg = 4. To enhance the anisotropy in the ground state, we suggest employing dichromatic optical HF pumping by adding a laser to excite D1 line 丨Fg = 4） → 丨Fe = 3） transition, in which the cesium magnetometer sensitivity increases by half a magnitude and is unaffected by the nonlinear Zeeman effect even in Earth＇s average magnetic field.
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.
Abstract This work investigates laser control of populations of magnetic sublevels of the ground hyperfine level of the cesium atom on the D2 line (6S1/2 → 6P3/2). A theoretical model is developed within the full density-matrix formalism based on the Lindblad equation, which accounts for coherent interaction with the laser field, spontaneous decay, and decoherence processes. The dynamics of the system is described by a set of coupled ordinary differential equations that reflect the complete Zeeman level structure and the competing relaxation channels characteristic of a realistic multilevel atomic medium. The aim of this work is the controlled redistribution and transfer of population between selected magnetic sublevels while minimizing the population of excited states. To this end, an optimization problem for the laser field parameters is formulated, including pulse amplitudes, frequency detunings, phases, and temporal profiles. Numerical calculations are performed by integrating the high-dimensional system of density-matrix evolution equations. The proposed approach constitutes a scalable computation platform for modeling and controlling Zeeman population dynamics in complex quantum systems and can be applied to problems of quantum state control and preparation.
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.