Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic and Molecular Physics

Saturation effects of transverse resonances in optical pumping experiments

Noriaki Tsukada, Y Murakami, T Ogawa

Published Dec 1, 1973• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/6/12/025

Related papers

Saturation effect in RF spectroscopy of transverse optical pumping

Noriaki Tsukada, Toru Ogawa

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.

Journal of Physics B Atomic and Molecular Physics•Aug 1, 1973•20 citations

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

Stig Stenholm, C.G. Aminoff

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.

Journal of Physics B Atomic and Molecular Physics•Nov 1, 1973•20 citations

Saturation effects in magnetic resonances for a general magnetic field configuration

Noriaki Tsukada, T. Koyama, Toru Ogawa

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.

Journal of Physics B Atomic and Molecular Physics•May 11, 1974•10 citations

Effect of Transverse Pumping in Optical Pumping

Noriaki Tsukada, T. Yabuzaki, Toru Ogawa

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.

Journal of the Physical Society of Japan•Sep 1, 1972•12 citations

Non-linear effects in optical pumping with lasers. I. General theory of the classical limit for levels of large angular momenta

M. Ducloy

The optical pumping of high J levels with a broad-band CW laser is studied theoretically. Exact non-perturbative solutions are obtained by means of a Fourier development of the response of the irradiated medium. This leads to such theoretical predictions as the depolarization of the fluorescence for high laser intensities, the power broadening of the Hanle effect and the appearance of a zero-field saturation resonance in the pi fluorescence. All these theoretical predictions are finally compared with recent experiments on the optical pumping of molecules especially Na 2 and I 2 .

Journal of Physics B Atomic and Molecular Physics•Feb 21, 1976•25 citations

Effect of Transverse Pumping in Two Rotating Fields

Noriaki Tsukada, T. Yabuzaki, Toru Ogawa

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.

Journal of the Physical Society of Japan•Jul 1, 1973•6 citations
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 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.
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.
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 optical pumping of high J levels with a broad-band CW laser is studied theoretically. Exact non-perturbative solutions are obtained by means of a Fourier development of the response of the irradiated medium. This leads to such theoretical predictions as the depolarization of the fluorescence for high laser intensities, the power broadening of the Hanle effect and the appearance of a zero-field saturation resonance in the pi fluorescence. All these theoretical predictions are finally compared with recent experiments on the optical pumping of molecules especially Na 2 and I 2 .
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.