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Journal of Physics B Atomic and Molecular Physics

Misalignment effects in magnetic resonance

David Thomas Pegg

Published Feb 1, 1973• 27 citations
Publisher

Abstract

By means of a theoretical approach recently developed by Pegg and Series (1970, 1973), the consequences of misalignment of the rotating field in magnetic resonance are investigated. Three main effects arise: a shift in the resonance frequency, a reduction in power broadening, and the appearance of 'multiple quantum' resonances at integral multiples of the rotating field frequency. For small misalignment angle theta , the misalignment shift is proportional to theta 4 and may be neglected in usual medium-precision experiments. The multiplicity of resonances should be readily detectable in optical pumping experiments.

DOI
10.1088/0022-3700/6/2/007

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Physical Review A•Jan 1, 1974•10 citations
By means of a theoretical approach recently developed by Pegg and Series (1970, 1973), the consequences of misalignment of the rotating field in magnetic resonance are investigated. Three main effects arise: a shift in the resonance frequency, a reduction in power broadening, and the appearance of 'multiple quantum' resonances at integral multiples of the rotating field frequency. For small misalignment angle theta , the misalignment shift is proportional to theta 4 and may be neglected in usual medium-precision experiments. The multiplicity of resonances should be readily detectable in optical pumping experiments.
By means of a theoretical approach recently developed by Pegg and Series, the consequences of misalignment of an oscillating rf field in optical-rf double resonances are investigated. Effects of both the longitudinal pumping and the transverse pumping are considered. We show that the single (or ordinary) or multiple quantum resonances and the transverse resonance appear at integral multiples of the oscillating field frequency simultaneously. It is also shown that there is no essential difference between the parametric resonance and the Haroche resonance, namely the transverse resonance becomes the parametric resonance for misalignment angle θ=90° and becomes the Haroche resonance for θ=0°.
Various magnetic resonances appearing in optical pumping experiments have been analysed theoretically and experimentally. However, there is little work on the saturation effects caused by strong RF fields. Recently, The saturation effects of the multiple quantum resonances and of the Haroche resonances have been investigated by Stenholm (1972) and by Tsukada and Ogawa (1973). The saturation effects are treated for the more general case of a static magnetic field in an arbitrary direction with respect to the oscillating RF field. The experimental results are compared with the exact solutions computed by the numerical integration of the Bloch equation. It is shown experimentally and theoretically that the resonances similar to the Haroche resonance appear at omega /sub ///=n omega , where omega /sub ///= gamma H/sub ///, n is an integer, H/sub /// is the parallel component of the static magnetic field with respect to the oscillating RF field, and gamma is the gyromagnetic ratio.
The evolution of magnetization of optically pumped atoms in the presence of two rotating rf fields with different frequencies is investigated by using the phenomenological Bloch equation. It is shown that the new type resonances, which are due to the effect of the transverse pumping, together with the ordinary magnetic resonance and the multiple quantum transitions are realized under these conditions. It is also shown that the Hanle curve is broadened by a rotating rf field in the same manner as by an oscillating rf field, and is shifted towards high field region as the intensity of the rotating rf field is increased. The results obtained are, in general, applicable to the case of an elliptically rotating rf field, which is superposition of two rotating rf fields.
A semi-classical approach developed by Pegg and Series (1970, 1973) is used to study higher order effects in magnetic resonance produced by an oscillating magnetic field perpendicular to a static field as the oscillating field strength is increased. It is shown that the well-known 'multiple quantum' transitions arise from a semi-classical theory, being transformed into 'single quantum' transitions induced by field harmonics in the most appropriate reference frame for treating the problem. Higher order terms in the Bloch-Siegert shift support those derived by Shirley (1965) by means of Floquet theory, and are in gross disagreement with those derived by Chang and Stehle (1971) from quantum electrodynamics, particularly at very high field intensities where the results are not even qualitatively similar. It should be possible to decide easily between the two approaches by experiment.
By means of the dressed atom concept examined theoretically by Cohen-Tannoudji and Haroche, the misalignment effects of an oscillating rf-field in optical-rf double resonances are investigated. We present a fully quantum mechanical calculation of higher-order effects in the frequency shifts of new coherence resonance for the general case that a spin-1/2 atom interacts with the oscillating rf-field in optical-pumping. It is analytically shown that the new type resonances can occur even by taking account of higher-order effects in the perturbation theory for the oscillating rf-field whose direction makes a special angle from that of a static field, and that the direction of the shift of the resonance field is not along that of the static field but perpendicular to that of the oscillating field. Theoretical results are compared with optical-pumping experiments of cesium vapor.
By expanding the atomic density matrix in powers of the light intensity, it is possible to derive simple formulas for the light shifts and optical broadening of magnetic-resonance lines in optical pumping experiments. Thus, we have obtained for the first time approximate analytic formulas for the light shifts in Zeeman multiplets with spins greater than 1/2. The predicted light shifts for a high-spin atom are similar to those for a spin-1/2 atom, and shifts due to real and virtual transitions can be identified. However, in contrast to the situation with a spin-1/2 atom, the light shifts for a high-spin atom depend on the magnitude of the rf field, and the shifts for the longitudinal and transverse components of orientation and alignment are not necessarily the same.