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Academic Symposium on Optoelectronics and Microelectronics Technology and Chinese-Russian Symposium on Laser Physics and Laser TechnologyOptoelectronics Technology

The time evolution for the populations of laser-pumped cesium atom Zeeman sublevels

Qingtao Wang, Chong Kang, Yang Zhang, Lei Cheng, Caiping Zheng, Jinku Lv

Published Jul 1, 2010• 2 citations
Publisher

Abstract

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.

DOI
10.1109/rcslplt.2010.5615295

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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.
The detecting principle of optical pumping cesium magnetometer sensor used for measurement of geomagnetic field is introduced. The population variation of the Zeeman sublevels with time in the laser-pumped cesium atoms is calculated from the approximate form of the optical Bloch equations, and the effect of laser detuning frequency and polarization state on the populations of Zeeman sublevels in cesium atoms is analyzed in detail. Matlab software is used to emulate the population variation curves in different laser detuning frequency and different polarization state. It is obtained from the curves that the polarization degree of cesium atoms is the most obvious and the optical pumping is the most efficient when the detuning frequency is 0 and the laser is left hand circularly polarized light. It is important to improve the detecting sensitivity and enhance the stability of optical pumping magnetometer sensor.
Abstract Incorporating the rate equations of the laser pumped atomic system, the population evolution of the Cesium Zeeman sublevels is calculated and discussed when a specific sequence of laser pulses irradiate the Cesium vapor. In this scheme, after the equalization of the sublevel populations by a magnetically resonant RF pulse, using a left (right) circularly polarized laser pulse the whole atomic population transfer to high (low) projection numbers. Then by irradiating a right (left) polarized laser pulse with appropriate duration and intensity, the desired population distribution could be obtained. The effects of different sequence parameters on the population distribution of Zeeman sublevels are investigated and it is shown that by proper process adjustment it is possible to arbitrary engineer the population distribution. Preparing the desired distribution of the population in the atomic sublevels is substantially important in different light–matter interaction experiments.
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 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.
Cs) atoms by applying circularly polarized light at an optimal frequency for electronic transitions from ground to excited states. To enhance control over sublevel populations following optical pumping, we incorporate a radiofrequency (RF) field. This integrated approach enables us to achieve a tailored distribution of atomic sublevel populations with high efficiency. Utilizing the Lindblad master equation, we provide a comprehensive framework for analyzing these dynamics, examining relaxation rates, repopulation processes, and the evolution of cesium Zeeman sublevels. Our findings underscore the effectiveness of the Lindblad master equation in accounting for external field effects and environmental interactions, significantly improving the accuracy and generalizability of optical pumping models. This method holds substantial promise for various applications in optical experiments, including magnetometry and quantum computing, paving the way for future advancements in these fields.
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.