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Journal of Physics B Atomic and Molecular Physics

Saturation effects in magnetic resonances for a general magnetic field configuration

Noriaki Tsukada, T. Koyama, Toru Ogawa

Published May 11, 1974• 10 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/7/7/016

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AIP Advances•May 1, 2020•3 citations
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.
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 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.
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.
The resonance behavior of magnetic and optical two-level systems under the influence of strong modulated fields is studied in detail by solving the Bloch equations in the limit of vanishing damping, namely, in terms of matrix continued fractions. Thus both analytical and numerical results are obtained for the positions of the various multiple quantum resonances in the time-averaged as well as modulated interaction components. Specifically, the role of the orientation of the optical pump beam in magnetic-resonance configurations is investigated, and it is shown that there are several classes of resonances for which the behavior of the system is independent of the orientation of the pump beam. These are the geometries in which the static and oscillating magnetic fields are either orthogonal or parallel, the geometries leading to Haroche-like resonances (which, however, play a special role in modulated interaction components also), and a previously unknown class, labeled saddle-point resonances. However, other than for these special classes, the behavior of the system depends generally on the orientation of the optical pump beam, unlike as implied in some previous work on this problem. As in the recently studied case of a fully amplitude-modulated optical interaction [W. M. Ruyten, Phys. Rev. A 40, 1447 (1989)], it is found that the resonances in modulated interaction components are generally doubly branched, with one branch duplicating the resonances found in the time-averaged component. A new feature found for not-fully-amplitude-modulated and phase-modulated, off-resonance optical excitation (or magnetic resonance with nonparallel or nonorthogonal static and oscillating magnetic fields) is the occurrence of an extra type of resonance in modulated components of the interaction that cannot, like all other resonances of the system, be classified as power-shifted multiple quantum transitions.
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°.
In this paper, we experimentally study the saturation effect of rubidium atomic magnetic resonance. A pump beam is applied to create atomic spin polarization, a radio frequency (RF) magnetic field is used to drive the spin precession about a static magnetic field, and an off-resonant linearly polarized probe beam is applied to detect the spin dynamics based on the Faraday-rotation effect. When the RF magnetic field intensity becomes strong, a saturation effect is observed. We measure the resonant peak under strong RF magnetic field driving and obtain a saturation dip as an indication of the saturation effect. Furthermore, we show that the line-width of the saturation dip is much smaller than that of magnetic resonance. Accordingly, the sensitivity of the precision measurement based on the saturation dip can be significantly improved. The relations between the saturation dip in the resonant peak and the driving RF magnetic field intensity, as well as pumping intensity, are also studied in our experiment.