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Journal of the Physical Society of Japan

Mixture of Longitudinal Resonance and Transverse Resonace

Noriaki Tsukada, Toru Ogawa

Published Mar 1, 1974• 3 citations
Publisher

Abstract

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°.

DOI
10.1143/jpsj.36.815

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Journal of Physics B Atomic and Molecular Physics•Nov 1, 1973•20 citations
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°.
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 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.
A theoretical and experimental study has been made of the effect of transverse optical pumping in the optical-rf double resonance of cesium atoms. The solution of Bloch type equations shows that the Hanle effect and new type resonances become notable in the weak magnetic field or for strong rf field, as the effect of the transverse pumping. The new type resonances appear in the unmodulated component and the components modulated at the first and the second harmonics of the applied rf frequency in the pumping light beam transmitted through the sample cell. It is predicted that the new type resonances are not only shifted but also broadened as the intensity of rf field increases. The shift, broadening and the intensity for observed new type resonances are in good agreement with the theoretical prediction.
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.
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.