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Journal of Experimental and Theoretical Physics

Characteristics of coherent population trapping in multilevel systems for magnetometry in plasma research

Valery Vdovin, Mikhail D. Tokman

Published Jun 1, 2010• 1 citation
Publisher

Abstract

An analysis is presented of the feasibility of measurements of local poloidal magnetic fields in toroidal magnetic fusion devices using coherent population trapping (CPT) in hydrogen-like probing atoms. A measurement scheme is examined in which CPT suppresses the resonance fluorescence from a probing beam of light neutrals with Zeeman-split levels. Feasibility requirements for CPT in three- and five-level systems are discussed. As a result, a theory of CPT-based magnetometry is developed for a system significantly more complex than the conventional three-level Λ system. A theoretical analysis shows that this technique can be used to measure a local safety factor in a toroidal device to an accuracy of a few percent.

DOI
10.1134/s1063776110060026

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An analysis is presented of the feasibility of measurements of local poloidal magnetic fields in toroidal magnetic fusion devices using coherent population trapping (CPT) in hydrogen-like probing atoms. A measurement scheme is examined in which CPT suppresses the resonance fluorescence from a probing beam of light neutrals with Zeeman-split levels. Feasibility requirements for CPT in three- and five-level systems are discussed. As a result, a theory of CPT-based magnetometry is developed for a system significantly more complex than the conventional three-level Λ system. A theoretical analysis shows that this technique can be used to measure a local safety factor in a toroidal device to an accuracy of a few percent.
Coherent population trapping (CPT) is theoretically examined as a magnetic-field diagnostic for high-\ensuremath{\beta} hydrogen plasma. Time-dependent quantum mechanical Bloch equations, which describe the evolution of the 2sss and 3ppp level populations of the hydrogen atom under CPT conditions, were solved numerically. When the frequency difference of two copropagating lasers equals the energy difference between the atoms' levels subject to the local magnetic field, a discernable CPT dark line in the H\ensuremath{\alpha} emission is predicted, enabling the possibility of noninvasive, localized magnetic-field measurements. The effects of fine and hyperfine level structure, Doppler broadening, plasma-generated electric fields, and degree-of-hydrogen ionization are included in the model. A shift in dark-line position of 15% of the linewidth is predicted to be caused by contributions from the entire H\ensuremath{\alpha} manifold. The laser-induced H\ensuremath{\alpha} fluorescence is estimated to be an order of magnitude stronger than the background H\ensuremath{\alpha} emission.
Summary form only given. We have experimentally investigated the potential of narrow coherent population trapping resonances for precision applications like magnetometry or atomic frequency standards. CPT can be observed in /spl Lambda/ systems where two ground states are coupled to a common excited state by two near-resonant light fields. Effective formation of ground state coherences takes place when the frequency difference of the light fields precisely matches the ground state splitting. This process leads to reduced absorption in the medium (electromagnetically induced transparency) and thus reduced fluorescence intensity (dark resonance) at the optical resonance frequency. Extremely narrow dark resonances can be observed when the two light fields have fixed phase and frequency difference and time-of-flight broadening is suppressed by the use of a buffer gas, making this type of system a promising candidate for precision applications. The /spl Lambda/ systems under study here are the D/sub 2/ lines of Cs, /sup 87/Rb and /sup 85/Rb where the ground state hyperfine splittings are 9.2 GHz, 6.8 GHz, and 3.0 GHz, respectively. Thus in a magnetic field the CPT resonance splits into several Zeeman components whose frequency positions are determined by the Breit-Rabi formula.
In the Λ three-level system, we will make use of semi-classical density matrix method to analyze cesium (Cs) hyperfine structure of coherent population trapping (CPT) phenomenon. Coherent population trapping has been widely used in electromagnetically induced transparency, non-inversion laser, optical storage and ultra-slow speed of light fields, then strong-coupling light and weak detecting light form coherent laser light to change the hyperfine structure energy levels of particles number distribution, which impacts on laser pumping magnetic resonance. In this paper, we will discuss the theoretical analysis and system design of laser pumping cesium magnetometer, cesium atomic energy level formed hyperfine structure with the I-J coupling, the hyperfine structure has been further split into Zeeman sublevels for the effects of magnetic field. To use laser pump and RF magnetic field make electrons transition in the Zeeman sublevels to produce the results of magneto-optical double resonance and on this basis we analyze the influence of laser pumping magnetic resonance based on coherent population trapping.
We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the nPnPnP manifold via an optical transition on one of the spectroscopic DDD lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.
Coherent population trapping (CPT) resonances on the degenerate two-level system of the (Fg=2→Fe=1) transition of the 87Rb D1 line were investigated in an uncoated vacuum cell by means of level-crossing type experiments-sweeping a magnetic field around zero value and using a single laser beam. The two-photon resonance manifests itself as fluorescence canceling when the system of levels is degenerate (at zero point of magnetic field). The influence of weak transverse magnetic fields on the amplitude and width of the resonance was investigated. The CPT resonances were observed with linear, circular and elliptical polarized laser light. Transverse magnetic field widens the resonances obtained by linear and circular polarization but splits the resonance created by slightly elliptically polarized laser light. The dependence of this splitting on the elliptical ratio and experimental geometry were investigated. Due to its narrow width and sensitivity to low magnetic fields (< 1 G) this resonance is very promising for small magnetic field measurement.