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Journal of Physics B Atomic and Molecular Physics

Saturation effect in RF spectroscopy of transverse optical pumping

Noriaki Tsukada, Toru Ogawa

Published Aug 1, 1973• 20 citations
Publisher

Abstract

The continued fraction method which has been adapted to the longitudinal optical pumping by Stenholm (1972) is used in a phenomenological Bloch equation to study the saturation effect of the Haroche's resonances, caused by the transverse pumping. The present authors give calculations of the positions and shapes of the Haroche's resonances for large intensity RF field, which differ from earlier work for a weak RF field by Cohen-Tannoudji and Haroche (1967). It is shown that the variation of the width of the Hanle curve by the oscillating RF field, i.e. the modification of the atomic g factor, is closely connected with the behaviour of the Haroche's resonances.

DOI
10.1088/0022-3700/6/8/041

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Saturation effects in RF spectroscopy. IV. Transverse pumping and Haroche's resonances

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Journal of the Physical Society of Japan•Jul 1, 1973•6 citations
The continued fraction method which has been adapted to the longitudinal optical pumping by Stenholm (1972) is used in a phenomenological Bloch equation to study the saturation effect of the Haroche's resonances, caused by the transverse pumping. The present authors give calculations of the positions and shapes of the Haroche's resonances for large intensity RF field, which differ from earlier work for a weak RF field by Cohen-Tannoudji and Haroche (1967). It is shown that the variation of the width of the Hanle curve by the oscillating RF field, i.e. the modification of the atomic g factor, is closely connected with the behaviour of the Haroche's resonances.
For pt.III, see abstr. A46187 of 1973. The authors solve the problem of a doublet excited state under the influence of an arbitrarily strong RF field and optically pumped by a transverse beam. The solution is obtained as a continued fraction, which is easily evaluated on a computer. Haroche's resonances at even multiples of the radio frequency are investigated and their Bloch-Siegert shifts are determined. The lines are less power broadened than the multi-photon resonances earlier investigated, and they are hence more exactly measurable. In the perturbation limit the authors regain results derived by Haroche and Cohen-Tannoudji from a quantum theory. Detection at either the DC component or any of the oscillating components is discussed. For the Hanle effect the authors find a generalization of the Cohen-Tannoudji dressed g-factor. The experimental results for a rotating RF field are discussed, and experiments using a linearly oscillating field performed by Tsukada, Yabuzaki and Ogawa are compared with the theory. Good agreement is found.
The results of the theory are compared with those of experiments for the transverse resonances, i.e. Haroche's resonances and the Hanle effect, in the presence of the strong RF field. It is shown theoretically and experimentally that Horoche's resonance are not only shifted but also broadened as the intensity of RF field is increased. The positions and the shapes of Haroche's resonances are related to the broadening of the Hanle curve due to the oscillating RF field. The positions of Haroche's resonance observed for large intensity of RF field agree well with those of the authors continued fraction solutions rather than those of the perturbation theory. The saturation effect of resonance intensity, which is due to large intensity RF field, is also verified theoretically and experimentally.
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 semiclassical description of an RF resonance measurement on a doublet excited state is formulated. The solution of the density matrix equation of motion is obtained as a continued fraction. The single quantum and multiple quantum transitions are seen as resonances in the measured quantities. An analytic solution is obtained for the case of degenerate doublet (the Hanle phenomena) and the RF modification of the g-value is obtained. It is shown that the continued fraction solution gives simple computations of strong field saturation effects.
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.