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Оптика и спектроскопия

Трехуровневое приближение при расчете параметров оптически детектируемого магнитного резонанса в условиях сильной лазерной накачки

Anton K. Vershovskii, Mikhail V. Petrenko

Published Jan 1, 2021• 2 citations
Publisher

Abstract

An algorithm is proposed for the approximate solution of a purely nonlinear problem of the parameters of optically detected magnetic resonance in the ground state of alkali atoms in an optically dense medium under conditions of intense narrow-band optical pumping, which causes, first, bleaching of the atomic medium, and, second, partial suppression of spin-exchange broadening. The direct solution of the Liouville equation under these conditions is complicated by the fact that the relaxation time of each of the levels of the hyperfine and Zeeman structure of the ground state is determined by the populations of the remaining levels, which leads to the necessity of solving a self-consistent problem in a multilevel system, and, as a rule, requires the use of supercomputers. In this paper, approximations are proposed that make it possible to significantly simplify and speed up the calculation by orders of magnitude, and the results are compared with experimental data using the example of a two-beam Mx scheme of a magnetometric sensor

DOI
10.21883/os.2021.04.50775.300-20

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Journal of Contemporary Physics (Armenian Academy of Sciences)•Jul 7, 2011•3 citations
An algorithm is proposed for the approximate solution of a purely nonlinear problem of the parameters of optically detected magnetic resonance in the ground state of alkali atoms in an optically dense medium under conditions of intense narrow-band optical pumping, which causes, first, bleaching of the atomic medium, and, second, partial suppression of spin-exchange broadening. The direct solution of the Liouville equation under these conditions is complicated by the fact that the relaxation time of each of the levels of the hyperfine and Zeeman structure of the ground state is determined by the populations of the remaining levels, which leads to the necessity of solving a self-consistent problem in a multilevel system, and, as a rule, requires the use of supercomputers. In this paper, approximations are proposed that make it possible to significantly simplify and speed up the calculation by orders of magnitude, and the results are compared with experimental data using the example of a two-beam Mx scheme of a magnetometric sensor
Abstract An algorithm of approximate solution of an essentially nonlinear problem of parameters of optically detected magnetic resonance in the ground state of alkali atoms in an optically dense medium under the conditions of strong narrow-band optical pumping that induces transparency of atomic medium and partial suppression of spin-exchange broadening is proposed. Straightforward solution of the Liouville’s equation is complicated in this case by the fact that relaxation time of each of the levels of the hyperfine and Zeeman structures of the ground state is determined by populations of all other levels, which results in the necessity of solving a self-consistent problem in a multilevel system and requires using supercomputers, as a rule. In the present work, approximations that allow substantially simplifying and accelerating calculation are proposed. A two-beam MX-scheme of a magnetometric sensor is used as an example to compare the results of calculations with experimental data.
An experimental comparison of the methods for modulating the parameters of resonant transverse to the external magnetic field pumping radiation in a two-beam optical magnetometric sensor (so called Bell-Bloom scheme) is carried out, as well as a comparison of these methods with the standard method of radio-frequency excitation of magnetic resonance under conditions of strong laser pumping. It is shown that although the standard method allows one to achieve a greater suppression of the spin-exchange broadening of the magnetic resonance line by pumping light, the Bell-Bloom scheme has advantages that make it possible to obtain similar sensitivity values upon modulation of both the intensity and polarization of the pump light; at the same time, the Bell-Bloom scheme is potentially characterized by higher speed, which is essential for the problems of magnetoencephalography and ultra-low field magnetic resonance imaging.
The ground electronic state of even such simple atoms as those of alkali elements has the set of sublevels. These sublevels are hyperfine (HF) components and magnetic sublevels. The collisions with particles of nonmagnetic buffer gas or even with walls (when walls have proper coating) do not mix practically the populations of ground state HF sublevels, if the orbital moment of electrons in the ground state is equal to zero. Due to this reason these sublevels may be extremely long lived. Because of this, for instance, the so-called effects of optical orientation and optical pumping are apparent in atoms of alkali metals. The radiation can pump practically all the atoms (with which there is effective interaction) to a single HF component. In a situation in which optical pumping is a minor effect, the monochromatic absorption line consists of separate lines corresponding to intra-atomic transitions. The optical pumping is not significant, for example, if the radiation intensity is so low that now pumping between HF sublevels occurs in the time it takes the atom to traverse the light beam. Under the conditions of optical pumping and when other nonlinear effects are present, the absorption line profile can undergo considerable alteration. Many theoretical and experimental investigations have been done in the laser spectroscopy of resonant transitions of atoms (atoms of alkali metals) under the conditions of optical pumping within ground state HF structure. A characteristic feature of all such investigations is the velocity-selective excitation of absorbing atoms. Also, as a rule, the value of HF splitting is not very big in comparison to Doppler broadening in these experiments. Under such conditions, the absorption spectra consists of Doppler- broadened lines with nonlinear resonances, which emerge when two fields of different frequencies or different propagation directions are employed. When only one monochromatic traveling wave is employed, optical pumping leads to formation of a single smooth absorption line occupying a position between the resonant transitions frequencies associated with HF components. As HF splitting grows, the line profile remains smooth, its width is approximately equal to the size of the HF splitting. The strength of the optical pumping from one ground state HF component to another is greater for greater HF splitting in comparison to the Doppler width. In this regard, Cs and Rb are the most typical of the alkali atoms (the HF splitting exceeds the Doppler width by a factor close to 20). This is the qualitative picture of the absorption line profile (particularly for a monochromatic radiation) under the conditions of optical pumping between the HF sublevels of the electronic ground state, this qualitative picture had formed by now.
Optimization of parameters of the M x resonance, which excited between Zeeman sublevels of a single HFS level of the ground state of an alkali metal in a vacuum cell in a circuit with a single beam for pumping and detection (M x magnetometer circuit), has been carried out. A simple model taking into account all main factors controlling the resolving power of the M x resonance (including spin-exchange broadening and absorption in a thick layer of the cell has been constructed. It is shown that the spin-resonance broadening of the resonance line is mainly determined by the requirements imposed on the optical thickness of the cell, which considerably restricts the realization of advantages of ultranarrow (<1 Hz) lines in magnetometry. The experiment confirming the efficiency of the model has been carried out.