ISSN 1063-7842, Technical Physics, 2008, Vol. 53, No. 5, pp. 646–654. © Pleiades Publishing, Ltd., 2008. Original Russian Text © A.K. Vershovskii, A.S. Pazgalev, 2008, published in Zhurnal Tekhnicheskoœ Fiziki, 2008, Vol. 78, No. 5, pp. 116–124. 646 INTRODUCTION The advances made in quantum magnetometry in the last five decades resulted in the development of a number of magnetometric devices based on optical pumping [1, 2] and optical detection [3] of magnetic resonance. The wide-range cesium magnetometer [4] and a more complicated but more precise potassium magnetometer operating on a single line [5–7] are appar- ently the most promising instruments for measuring the magnitude of terrestrial magnetic fields (20–80 μT). Both these instruments belong to the class of M x magnetom- eters since beam modulation of optical pump by the transverse component of the rotating magnetic moment during the interaction with a resonant radio-frequency field (M x resonance) is used as the observed signal in the circuits of these instruments. The sensitivity of such instruments is entirely controlled by the magnetic reso- nance parameters and quantum noise that cannot be eliminated in principle. This study aims at optimization of the parameters of the M x resonance, which is excited between Zeeman sublevels of the same 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. The main factors determining the resolving power of the M x resonance, including spin-exchange broadening and absorption in a thick layer of the cell, are taken into account in opti- mization. The exact solution of the problem of optimization of resonance parameters in a multilayer system involves considerable difficulties (see, for example, [8]) since it necessitates the inclusion of the dependence of absorp- tion in the cell as well as of optical and collision broad- ening on the degree of polarization of the substance, which is in turn determined by pumping conditions. We will consider optical pumping in a cell with an antire- laxation coating, in which level “mixing” in the excited state is negligibly small. In this case, the problem can be solved exactly only using numerical methods. How- ever, we set out to construct a simple analytical model having a clear physical meaning and capable of provid- ing correct quantitative predictions. It will be shown that such a model can be constructed in the framework of the following approximations. (1) Magnetic resonance is described by the Bloch equations [9] for a two-level system. This approxima- tion is justified for (i) the K atom in high (terrestrial) magnetic fields since the high degree of isolation of its resonance line makes it possible to consider magnetic resonance only between two energy levels of the “working” transition (F = 2, m F = 1 F = 2, m F = 2), provided that the total population of these levels is smaller than unity. Numer- ical analysis shows that the difference in the occupan- cies of this pair of levels for the optimal intensity of pump light amounts to approximately 0.5, while the sum (denoted by k pump ) is k pump ≈ 0.75; (ii) for all alkali metals (including Cs) in the oppo- site case of weak magnetic fields, in which quadratic Zeeman splitting is smaller than the intrinsic linewidth (this case is realized for cesium when the magnetic field induction does not exceed 20 μT). (2) Spin-exchange broadening of the resonance line is assumed to be independent of the degree of polariza- tion of the working substance Optimization of the Q Factor of the Magnetic M x Resonance under Optical Pump Conditions A. K. Vershovskii and A. S. Pazgalev Ioffe Physicotechnical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia e-mail: antver@mail.ru Received June 28, 2007 Abstract—Optimization of parameters of the M x resonance, which excited between Zeeman sublevels of a sin- gle 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 absorp- tion in a thick layer of the cell has been constructed. It is shown that the spin-resonance broadening of the res- onance line is mainly determined by the requirements imposed on the optical thickness of the cell, which con- siderably restricts the realization of advantages of ultranarrow (<1 Hz) lines in magnetometry. The experiment confirming the efficiency of the model has been carried out. PACS numbers: 07.55.Ge DOI: 10.1134/S1063784208050198 EXPERIMENTAL INSTRUMENTS AND TECHNIQUE