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Symmetry

Analytical Solutions of Temporal Evolution of Populations in Optically-Pumped Atoms with Circularly Polarized Light

Heung‐Ryoul Noh

Published Mar 19, 2016• 4 citations
Publisher

Abstract

We present an analytical calculation of temporal evolution of populations for optically pumped atoms under the influence of weak, circularly polarized light. The differential equations for the populations of magnetic sublevels in the excited state, derived from rate equations, are expressed in the form of inhomogeneous second-order differential equations with constant coefficients. We present a general method of analytically solving these differential equations, and obtain explicit analytical forms of the populations of the ground state at the lowest order in the saturation parameter. The obtained populations can be used to calculate lineshapes in various laser spectroscopies, considering transit time relaxation.

DOI
10.3390/sym8030017

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We present an analytical calculation of temporal evolution of populations for optically pumped atoms under the influence of weak, circularly polarized light. The differential equations for the populations of magnetic sublevels in the excited state, derived from rate equations, are expressed in the form of inhomogeneous second-order differential equations with constant coefficients. We present a general method of analytically solving these differential equations, and obtain explicit analytical forms of the populations of the ground state at the lowest order in the saturation parameter. The obtained populations can be used to calculate lineshapes in various laser spectroscopies, considering transit time relaxation.
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.
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 an analytic calculation of the population of each magnetic sublevel of the 87Rb^{87}\mathrm{Rb}87Rb atom. Under the influence of a weak circularly polarized laser beam, the rate equations governing the internal dynamics of this atom were solved analytically and the results were compared with numerical calculations. As far as the condition of low intensity is satisfied, it is possible to obtain exact analytic populations regardless of the magnitude of energy spacings, transition lines, and laser polarization (circular or linear).
By solving the optical Bloch equations with the rate-equation approximation, we calculate the time dependence of the magnetic sublevel populations of Doppler-broadened atoms. With an increase of the left-circularly polarized pump intensity, the population fraction of a certain sublevel of the excited state almost reaches 0.3, resulting in anisotropy in the excited state, which is important to the optical filter based on circular birefringence and dichroism. Furthermore, numerical results show that the real saturation pump intensity for the moving atoms is much larger than that for the resting atoms.
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.