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Technical Physics

Optimization of the Q factor of the magnetic M x resonance under optical pump conditions

Anton K. Vershovskii, Anatoly S. Pazgalev

Published May 1, 2008• 26 citations
Publisher

Abstract

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.

DOI
10.1134/s1063784208050198

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Optical Methods of Atomic Orientation and of Magnetic Resonance*

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In the optical excitation of atoms with polarized light, producing excited atoms, only some of the Zeeman sublevels of the excited state are actually reached, so that large differences of population can be built up between Zeeman sublevels or between hyperfine structure (hfs) levels. This property can be used to detect radio-frequency resonance in optically excited atomic states. These resonances produce a characteristic change in intensity or in the degree of polarization of the light re-emitted. Zeeman intervals, Stark effects, and hfs intervals can be measured in this manner. (The Stark constant of the 63P1 level of Hg and the electric quadrupole moments of the alkali atoms have been obtained in this way.)The technique of “optical pumping” gives a way to concentrate atoms in some of the Zeeman sublevels of one of the hfs levels of the ground state.Atomic orientation has been obtained with the Na atom, in an atomic beam and in the vapor in equilibrium with the metal. The orientation effects have been studied by detection of radio-frequency resonance signals in the ground state. Orientation can be increased many times by adding a variable pressure of a foreign gas to the pure Na vapor. Because of the coupling between nuclear spin and electron spin, nuclear orientation is produced at the same time as atomic orientation.

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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.
The hybrid optical pumping atomic magnetometers have not realized its theoretical sensitivity, the optimization is critical for optimal performance. The optimizations proposed in this paper are suitable for hybrid optical pumping atomic magnetometer, which contains two alkali species. To optimize the parameters, the dynamic equations of spin evolution with two alkali species were solved, whose steady-state solution is used to optimize the parameters. The demand of the power of the pump beam is large for hybrid optical pumping. Moreover, the sensitivity of the hybrid optical pumping magnetometer increases with the increase of the power density of the pump beam. The density ratio between the two alkali species is especially important for hybrid optical pumping magnetometer. A simple expression for optimizing the density ratio is proposed in this paper, which can help to determine the mole faction of the alkali atoms in fabricating the hybrid cell before the cell is sealed. The spin-exchange rate between the two alkali species is proportional to the saturated density of the alkali vapor, which is highly dependent on the temperature of the cell. Consequently, the sensitivity of the hybrid optical pumping magnetometer is dependent on the temperature of the cell. We proposed the thermal optimization of the hybrid cell for a hybrid optical pumping magnetometer, which can improve the sensitivity especially when the power of the pump beam is low. With these optimizations, a sensitivity of approximately 5 fT/Hz(1/2) is achieved with gradiometer arrangement.
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.
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.
A generalized model for the magnetic resonance signal corresponding to the 0-0 hyperfine transition in an optically pumped alkali-metal vapor is presented. Under conditions of microwave power broadening, the model predicts ``anomalous'' light broadening and ``anomalous'' relaxation narrowing of the magnetic resonance linewidth. Good agreement between theory and experiment was obtained in an experiment that confirmed the prediction of anomalous light broadening. These results show that the 0-0 hyperfine transition cannot be described as a simple two-level system; rather, the alkali-atom's nuclear spin plays an important role in determining the magnetic resonance linewidth.
We present the results of studying the parameters of the magnetic MX{M}_{X}MX​ resonance in an all-optical sensor built according to the two-beam Bell-Bloom scheme in nonzero ultraweak magnetic fields in which the effects of spin-exchange broadening suppression are partially manifested. We report on the features of the resonance under these conditions. We also optimize the resonance parameters to achieve maximum sensitivity in magnetoencephalographic sensors. We demonstrate an improvement in the ultimate achievable sensitivity of an all-optical MX{M}_{X}MX​ sensor by a factor of 4 or more, which in our experiment corresponds to a decrease from 13 to 3fT/Hz1/23\phantom{\rule{0.2em}{0ex}}{\text{fT/Hz}}^{1/2}3fT/Hz1/2 in a volume of 0.13cm30.13\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{3}0.13cm3. We also report the effect of incomplete suppression of spin-exchange broadening under conditions of strong transverse modulated optical pumping, and propose a semiempirical model to describe it.
In the optical excitation of atoms with polarized light, producing excited atoms, only some of the Zeeman sublevels of the excited state are actually reached, so that large differences of population can be built up between Zeeman sublevels or between hyperfine structure (hfs) levels. This property can be used to detect radio-frequency resonance in optically excited atomic states. These resonances produce a characteristic change in intensity or in the degree of polarization of the light re-emitted. Zeeman intervals, Stark effects, and hfs intervals can be measured in this manner. (The Stark constant of the 63P1 level of Hg and the electric quadrupole moments of the alkali atoms have been obtained in this way.)The technique of “optical pumping” gives a way to concentrate atoms in some of the Zeeman sublevels of one of the hfs levels of the ground state.Atomic orientation has been obtained with the Na atom, in an atomic beam and in the vapor in equilibrium with the metal. The orientation effects have been studied by detection of radio-frequency resonance signals in the ground state. Orientation can be increased many times by adding a variable pressure of a foreign gas to the pure Na vapor. Because of the coupling between nuclear spin and electron spin, nuclear orientation is produced at the same time as atomic orientation.