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 in RF spectroscopy. I. General theory

Stig Stenholm

Published Apr 1, 1972• 110 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/5/4/023

Related papers

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 RF spectroscopy. III. Mixing of nearly degenerate levels by strong off-resonant fields

Stig Stenholm

For pt. II see abstr. A31645 of 1972. The author solves the problem of a strong RF field interacting with a degenerate doublet in terms of complex order Bessel functions. The influence of phenomenological pumping and decay parameters is displayed. The solution is compared to numerical results obtained from the previously published continued fraction solution.

Journal of Physics B Atomic and Molecular Physics•Jun 1, 1973•13 citations

Saturation Effects of a Two-Level System in Two RF Fields

Noriaki Tsukada

The purpose of this paper is to develop a theory of saturation effects of the two-level system in two rotating rf fields with different frequencies and arbitrary intensities. We analyze this problem with the density matrix equation of motion including the relaxation processes, and the solution is obtained in the form of continued fraction. We give numerical calculations of the positions and shapes of the single and multiple quantum resonances, caused by large intensity rf fields using this continued fraction solution. It is also shown that the irradiation of an atomic system with a saturating field quasiresonant to a given transition drastically changes the absorption line shape of a probe field.

Journal of the Physical Society of Japan•Apr 15, 1979•17 citations

Matrix continued-fraction solution for saturation effects in spin-½ radio-frequency spectroscopy

M. Allegrini, E. Arimondo, Arturo Bambini

We present a semiclassical solution for a Zeeman-split, optically pumped, spin-\textonehalf{} system interacting with a strong radio-frequency field. The method of solution presented here is based upon a matrix continued-fraction expansion, and can explain any resonance phenomena which occur for arbitrary geometrical configurations of the pumping beam or the rf field polarization axis. Theoretical predictions of line shapes for some cases are reported and discussed. The solution can also explain some deviations of the observed Bloch-Siegert shift at high rf power from the behavior predicted by a previous semiclassical theory, which can account for simple geometrical configurations only.

Physical Review A•Feb 1, 1977•18 citations

Saturation effects in RF spectroscopy. II. Multiple quantum transitions

Stig Stenholm

For Pt. I see ibid., vol.5, no.4, 878. The author presents calculations of the positions and shapes of the multiple quantum resonances, caused by a large intensity RF field, using a continued fraction solution presented in an earlier paper. The shift of the line is given for up to 11 quantum transitions and the width up to 7 quantum transitions. It is shown in which parameter ranges the results differ from earlier work by Shirley and Cohen-Tannoudji and Haroche.

Journal of Physics B Atomic and Molecular Physics•Apr 1, 1972•72 citations

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
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.
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 purpose of this paper is to develop a theory of saturation effects of the two-level system in two rotating rf fields with different frequencies and arbitrary intensities. We analyze this problem with the density matrix equation of motion including the relaxation processes, and the solution is obtained in the form of continued fraction. We give numerical calculations of the positions and shapes of the single and multiple quantum resonances, caused by large intensity rf fields using this continued fraction solution. It is also shown that the irradiation of an atomic system with a saturating field quasiresonant to a given transition drastically changes the absorption line shape of a probe field.
We present a semiclassical solution for a Zeeman-split, optically pumped, spin-\textonehalf{} system interacting with a strong radio-frequency field. The method of solution presented here is based upon a matrix continued-fraction expansion, and can explain any resonance phenomena which occur for arbitrary geometrical configurations of the pumping beam or the rf field polarization axis. Theoretical predictions of line shapes for some cases are reported and discussed. The solution can also explain some deviations of the observed Bloch-Siegert shift at high rf power from the behavior predicted by a previous semiclassical theory, which can account for simple geometrical configurations only.
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.