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

Aligned atoms in strong oscillating RF fields. I. The unmodulated resonance signals

E Jacobson

Published Sep 28, 1980• 2 citations
Publisher

Abstract

In radio frequency (RF) experiments on aligned atoms (e.g. optical double resonance) new phenomena can be found in the case of longitudinal excitation if a strong oscillating RF field is used: both the positions of the RF resonances (RF shift) and the widths (power broadening) depend on the direction of the light observed and on the state of its (linear) polarisation. This applies to the main (single-quantum) transitions as well as the (odd) multi-quanta transitions. These effects have been observed in an experiment on aligned mercury atoms in the metastable 6 3 P 2 state and have been confirmed by numerical calculations based on the semiclassical approach.

DOI
10.1088/0022-3700/13/18/010

Related papers

Aligned atoms in strong oscillating RF fields. II. Modulation signals

E Jacobson

For pt.I see ibid., vol.13, p.3577 (1980). In a radio frequency (RF) experiment on aligned atoms modulation signals have been observed containing high-order harmonics of the fundamental RF (up to the 13th). The amplitudes of these harmonics have been investigated as a function of the static magnetic field over a wide range. Resonance structures have been found which are related to single- and (odd) multi-quanta transitions as well. The measurements are in good agreement with numerical calculations based on the semiclassical approach.

Journal of Physics B Atomic and Molecular Physics•Sep 28, 1980•1 citation

Interrelationship between the polarization moments of different parity upon optical pumping of atoms under the magnetic resonance conditions: I. Experiment on the 133Cs and 4He atoms

N. A. Dovator, A. I. Okunevich

In an experiment with an optical pumping of 133Cs atoms in the 62 S 1/2 ground state, the line shape of the D 2f magnetic resonance signal for the transverse alignment component oscillating at a double frequency f of a radio-frequency (RF) magnetic field is found to strongly depend on the polarization of pumping radiation. On passage from a linearly polarized pumping light to a circularly polarized (CP) light with a sufficiently strong RF field the ordinary three-peak line with the highest central peak transforms into a two-peak line with a minimum at the center, so that the D 2f signal line resembles the M f signal line of a transverse orientation oscillating at the RF field frequency f. This suggests that the orientation (the first-rank polarization moment (PM)) arising upon CP pumping affects the alignment (the second-rank PM); i.e., the PMs of Cs atoms with different parities of their ranks become coupled. No influence of the polarization of a pumping radiation on the line shape of the D 2f signal is observed in a similar experiment with the 4He atoms in the 23 S 1 metastable state.

Optics and Spectroscopy•Apr 1, 2007•2 citations

High-order magnetic resonance in the presence of strong longitudinal radio-frequency magnetic field based on atomic alignment states

Tao Shi, Ge Jin, Sheng Zou

A longitudinal radio-frequency (rf) magnetic field resonating at the Larmor frequency along the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ direction in the presence of a static transverse magnetic field s investigated. Optical-radio-frequency double resonance in $^{85}\mathrm{Rb}$ characterizes the strength of an external magnetic field through the precession frequency of $^{85}\mathrm{Rb}$ atoms. The measurements are carried out in a paraffin-coated $^{85}\mathrm{Rb}$ cell with a spin alignment configuration. An intriguing discovery of magnetic resonance peaks is observed at subharmonics of the Larmor frequency, accompanied by the emergence of nonlinear effects in the vicinity of the resonance. Notably, when the Larmor frequency reaches zero, the optical rotation signals induced by the rf magnetic field demonstrate a superposition of high-order harmonics of the rf frequency. Based on the simplified density matrix formalism and perturbation treatment, analytical expressions for the optical rotation are consistent with experimental outcomes. These findings hold the potential of extending our understanding on unveiling the dynamics of population and coherence among Zeeman sublevels, thereby advancing our knowledge in the field of alignment magnetometry.

Physical Review A•Apr 26, 2024•10 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

Theory of modulation of light in a double resonance experiment

John N. Dodd, George William Series

Abstract A theory is formulated to describe the modulation which has been observed in fluorescent light from atoms subjected simultaneously to optical and radio-frequency radiation. The optical field stimulates one or more of a set of excited states of the atom, between which the radio-frequency field establishes coherence. This coherence is manifest in the fluorescent radiation. Interference between radiations of different frequency leads to modulation. General expressions are given for the intensity of the fluorescent light as a function of time. The Zeeman structure of the transition (63P1 — 6 1S0), A2537 A, in mercury is studied in detail. Modulation at frequencies, 1, 2, 3 and 4 times that of the radio-frequency field, w0, is predicted, and resonant effects at static magnetic fields, 0, 1/2, 1, 3/2, 2 and 3 times H0, the field for which w0 is the Larm or frequency. Resonances at fields other than H0 are due to excitation with light of mixed polarization. Most of the predicted effects have been found experimentally. A ‘frequency diagram’ is introduced and discussed, to represent the combined effects of static and radio-frequency magnetic fields. To each excited state belong a set of r frequencies, where r is the number of states linked by the radio-frequency perturbation. The 9 levels are drawn, as functions of H, for the states mJ = 0, ± 1, of 3P1. The resonances at fields other than H0 may be associated with intersections of frequency levels belonging to different mJ.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Sep 19, 1961•106 citations

Single magneto-optical resonance in a modulated RF field

Eugene A. Tsygankov, Sergei A. Zibrov, Alexander S. Zibrov +6 more

A symmetric magneto-optical resonance arising from the single two-quantum RF transition $|{F}_{g}=1,{m}_{{F}_{g}}=\ensuremath{-}1\ensuremath{\rangle}\ensuremath{\leftrightarrows}|{F}_{g}=1,\phantom{\rule{4pt}{0ex}}{m}_{{F}_{g}}=1\ensuremath{\rangle}$ in an optically aligned atomic ensemble is studied in the case when the quadratic Zeeman shift exceeds the width of the resonance. It is shown that the signal-to-noise ratio of the resonance can be significantly increased by applying the phase modulation to the RF field at a frequency close to the value of quadratic Zeeman shift. This theoretical prediction is corroborated by the experimental results with $^{87}\mathrm{Rb}$ atoms. The proposed technique can be used in magnetometers based on atomic alignment or by utilizing multiquantum RF resonances in optically oriented atomic ensembles.

Physical Review A•Jun 26, 2019•5 citations
In radio frequency (RF) experiments on aligned atoms (e.g. optical double resonance) new phenomena can be found in the case of longitudinal excitation if a strong oscillating RF field is used: both the positions of the RF resonances (RF shift) and the widths (power broadening) depend on the direction of the light observed and on the state of its (linear) polarisation. This applies to the main (single-quantum) transitions as well as the (odd) multi-quanta transitions. These effects have been observed in an experiment on aligned mercury atoms in the metastable 6 3 P 2 state and have been confirmed by numerical calculations based on the semiclassical approach.
For pt.I see ibid., vol.13, p.3577 (1980). In a radio frequency (RF) experiment on aligned atoms modulation signals have been observed containing high-order harmonics of the fundamental RF (up to the 13th). The amplitudes of these harmonics have been investigated as a function of the static magnetic field over a wide range. Resonance structures have been found which are related to single- and (odd) multi-quanta transitions as well. The measurements are in good agreement with numerical calculations based on the semiclassical approach.
In an experiment with an optical pumping of 133Cs atoms in the 62 S 1/2 ground state, the line shape of the D 2f magnetic resonance signal for the transverse alignment component oscillating at a double frequency f of a radio-frequency (RF) magnetic field is found to strongly depend on the polarization of pumping radiation. On passage from a linearly polarized pumping light to a circularly polarized (CP) light with a sufficiently strong RF field the ordinary three-peak line with the highest central peak transforms into a two-peak line with a minimum at the center, so that the D 2f signal line resembles the M f signal line of a transverse orientation oscillating at the RF field frequency f. This suggests that the orientation (the first-rank polarization moment (PM)) arising upon CP pumping affects the alignment (the second-rank PM); i.e., the PMs of Cs atoms with different parities of their ranks become coupled. No influence of the polarization of a pumping radiation on the line shape of the D 2f signal is observed in a similar experiment with the 4He atoms in the 23 S 1 metastable state.
A longitudinal radio-frequency (rf) magnetic field resonating at the Larmor frequency along the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ direction in the presence of a static transverse magnetic field s investigated. Optical-radio-frequency double resonance in 85Rb^{85}\mathrm{Rb}85Rb characterizes the strength of an external magnetic field through the precession frequency of 85Rb^{85}\mathrm{Rb}85Rb atoms. The measurements are carried out in a paraffin-coated 85Rb^{85}\mathrm{Rb}85Rb cell with a spin alignment configuration. An intriguing discovery of magnetic resonance peaks is observed at subharmonics of the Larmor frequency, accompanied by the emergence of nonlinear effects in the vicinity of the resonance. Notably, when the Larmor frequency reaches zero, the optical rotation signals induced by the rf magnetic field demonstrate a superposition of high-order harmonics of the rf frequency. Based on the simplified density matrix formalism and perturbation treatment, analytical expressions for the optical rotation are consistent with experimental outcomes. These findings hold the potential of extending our understanding on unveiling the dynamics of population and coherence among Zeeman sublevels, thereby advancing our knowledge in the field of alignment magnetometry.
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.
Abstract A theory is formulated to describe the modulation which has been observed in fluorescent light from atoms subjected simultaneously to optical and radio-frequency radiation. The optical field stimulates one or more of a set of excited states of the atom, between which the radio-frequency field establishes coherence. This coherence is manifest in the fluorescent radiation. Interference between radiations of different frequency leads to modulation. General expressions are given for the intensity of the fluorescent light as a function of time. The Zeeman structure of the transition (63P1 — 6 1S0), A2537 A, in mercury is studied in detail. Modulation at frequencies, 1, 2, 3 and 4 times that of the radio-frequency field, w0, is predicted, and resonant effects at static magnetic fields, 0, 1/2, 1, 3/2, 2 and 3 times H0, the field for which w0 is the Larm or frequency. Resonances at fields other than H0 are due to excitation with light of mixed polarization. Most of the predicted effects have been found experimentally. A ‘frequency diagram’ is introduced and discussed, to represent the combined effects of static and radio-frequency magnetic fields. To each excited state belong a set of r frequencies, where r is the number of states linked by the radio-frequency perturbation. The 9 levels are drawn, as functions of H, for the states mJ = 0, ± 1, of 3P1. The resonances at fields other than H0 may be associated with intersections of frequency levels belonging to different mJ.
A symmetric magneto-optical resonance arising from the single two-quantum RF transition $|{F}_{g}=1,{m}_{{F}_{g}}=\ensuremath{-}1\ensuremath{\rangle}\ensuremath{\leftrightarrows}|{F}_{g}=1,\phantom{\rule{4pt}{0ex}}{m}_{{F}_{g}}=1\ensuremath{\rangle}$ in an optically aligned atomic ensemble is studied in the case when the quadratic Zeeman shift exceeds the width of the resonance. It is shown that the signal-to-noise ratio of the resonance can be significantly increased by applying the phase modulation to the RF field at a frequency close to the value of quadratic Zeeman shift. This theoretical prediction is corroborated by the experimental results with 87Rb^{87}\mathrm{Rb}87Rb atoms. The proposed technique can be used in magnetometers based on atomic alignment or by utilizing multiquantum RF resonances in optically oriented atomic ensembles.