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Proceedings of NAS RA Physics

Оптимизация параметров лазерного поля для управления населённостями магнитных подуровней в многоуровневой системе Cs D₂

Р. Саакян, E. A. Gazazyan

Published Jul 27, 2025• 0 citations
Publisher

Abstract

This work investigates laser control of the populations of magnetic sublevels of the ground hyperfine level of cesium atoms in the D₂ line D₂ (6S₁/₂ → 6P₃/₂). The theoretical model is formulated within the full density matrix formalism based on the Lindblad master equation, which accounts for coherent interaction with the laser field, spontaneous decay, and decoherence processes. The system dynamics is described by a set of coupled ordinary differential equations representing the complete Zeeman structure of the levels and the competing relaxation channels characteristic of a realistic multilevel atomic system. The main objective of this study is the controlled redistribution and transfer of population between selected magnetic sublevels while minimizing the population of excited states. To achieve this goal, an optimization problem for the laser field parameters is formulated, including amplitudes, frequency detunings, phases, and temporal pulse profiles. Numerical simulations are performed by integrating a high-dimensional system of evolution equations for the density matrix elements. The proposed approach provides a scalable computational framework for modeling and controlling Zeeman population dynamics in complex quantum systems and can be applied to problems of coherent control and quantum state preparation.

DOI
10.54503/0002-3035-2026-61.2-209

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This work investigates laser control of the populations of magnetic sublevels of the ground hyperfine level of cesium atoms in the D₂ line D₂ (6S₁/₂ → 6P₃/₂). The theoretical model is formulated within the full density matrix formalism based on the Lindblad master equation, which accounts for coherent interaction with the laser field, spontaneous decay, and decoherence processes. The system dynamics is described by a set of coupled ordinary differential equations representing the complete Zeeman structure of the levels and the competing relaxation channels characteristic of a realistic multilevel atomic system. The main objective of this study is the controlled redistribution and transfer of population between selected magnetic sublevels while minimizing the population of excited states. To achieve this goal, an optimization problem for the laser field parameters is formulated, including amplitudes, frequency detunings, phases, and temporal pulse profiles. Numerical simulations are performed by integrating a high-dimensional system of evolution equations for the density matrix elements. The proposed approach provides a scalable computational framework for modeling and controlling Zeeman population dynamics in complex quantum systems and can be applied to problems of coherent control and quantum state preparation.
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.
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.
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.
Coherent-population-trapping resonance in vapor cell is a quantum interference effect that appears in the two-photon transitions between the ground-state hyperfine levels of alkali-metal atoms and is often utilized in miniature and centimeter-scale clock devices. To quantitatively understand and predict the performance of this phenomenon, it is necessary to consider the transitions and relaxations between all hyperfine Zeeman sublevels involved in the different excitation processes of the atom. In this paper, we constructed a computational multilevel atomic model of the Liouville density-matrix equation for 32 Zeeman sublevels involved in the D1{D}_{1}D1​ line of 133Cs^{133}\mathrm{Cs}133Cs irradiated by two frequencies with circularly polarized components and then simulated the amplitude and shape of the resonance spectrum of the transmitted light through centimeter-scale Cs-vapor cells. We show that the numerical solutions of the equation and analytical investigations adequately explain a variety of the characteristics observed in the experiment.
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.