In a previous paper, I have presented a general theory of the optical pumping of atoms by a polarized multimode-laser beam, in the presence of a magnetic field. Equations of motion, valid at arbitrary laser intensities for the density matrix of the atomic system, have been obtained. In this paper, these equations are exactly solved for a linearly $\ensuremath{\sigma}$-polarized laser and levels having small angular momenta. More precisely, I consider the laser transitions ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=0$, ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=1$, and ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$. Two particular results are emphasized: (i) For $J=1\ensuremath{-}J=0$ and $J=1\ensuremath{-}J=1$ transitions and for the $J=2$ level of a $J=1\ensuremath{-}J=2$ transition, the laser-induced Hanle effects keep a Lorentzian shape, independent of the laser intensity. For the $J=1\ensuremath{-}J=1$ transition, it is shown that the depolarizing relaxation processes play a leading part in the coupling induced by the laser between the transverse alignments of the two levels. On the other hand, the power broadenings of the Hanle effects are shown to be similar. For the $J=1$ level of a $J=1\ensuremath{-}J=2$ transition, the Hanle-effect shape presents a departure from the Lorentzian one, owing to a coupling with the laser-induced hexadecapole moment in the $J=2$ level. (ii) The populations of the levels exhibit a "zero-field saturation resonance" which is due to the coupling with the Zeeman coherences. These resonances, which reproduce the Hanle effects of the transition, can be observed on the $\ensuremath{\pi}$-polarized fluorescence from the levels. In general, these resonances appear as a saturation effect, i.e., they reduce the laser-induced fluorescence of the levels in zero magnetic field. However, for the ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$ transition, the ${J}_{a}=2\ensuremath{\rightarrow}{J}_{f}=2 \ensuremath{\pi}$ fluorescence presents an anomalous behavior; the saturation resonance increases the zero-field laser-induced fluorescence. The theoretical study shows the prominent part played by the value of the ${J}_{b}=1$ level lifetime in the interpretation of this anomaly. Other results, such as the laser-induced depolarization of the fluorescence, are also obtained. All the theoretical predictions have been experimentally checked and will be presented in forthcoming papers.In a previous paper, I have presented a general theory of the optical pumping of atoms by a polarized multimode-laser beam, in the presence of a magnetic field. Equations of motion, valid at arbitrary laser intensities for the density matrix of the atomic system, have been obtained. In this paper, these equations are exactly solved for a linearly $\ensuremath{\sigma}$-polarized laser and levels having small angular momenta. More precisely, I consider the laser transitions ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=0$, ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=1$, and ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$. Two particular results are emphasized: (i) For $J=1\ensuremath{-}J=0$ and $J=1\ensuremath{-}J=1$ transitions and for the $J=2$ level of a $J=1\ensuremath{-}J=2$ transition, the laser-induced Hanle effects keep a Lorentzian shape, independent of the laser intensity. For the $J=1\ensuremath{-}J=1$ transition, it is shown that the depolarizing relaxation processes play a leading part in the coupling induced by the laser between the transverse alignments of the two levels. On the other hand, the power broadenings of the Hanle effects are shown to be similar. For the $J=1$ level of a $J=1\ensuremath{-}J=2$ transition, the Hanle-effect shape presents a departure from the Lorentzian one, owing to a coupling with the laser-induced hexadecapole moment in the $J=2$ level. (ii) The populations of the levels exhibit a "zero-field saturation resonance" which is due to the coupling with the Zeeman coherences. These resonances, which reproduce the Hanle effects of the transition, can be observed on the $\ensuremath{\pi}$-polarized fluorescence from the levels. In general, these resonances appear as a saturation effect, i.e., they reduce the laser-induced fluorescence of the levels in zero magnetic field. However, for the ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$ transition, the ${J}_{a}=2\ensuremath{\rightarrow}{J}_{f}=2 \ensuremath{\pi}$ fluorescence presents an anomalous behavior; the saturation resonance increases the zero-field laser-induced fluorescence. The theoretical study shows the prominent part played by the value of the ${J}_{b}=1$ level lifetime in the interpretation of this anomaly. Other results, such as the laser-induced depolarization of the fluorescence, are also obtained. All the theoretical predictions have been experimentally checked and will be presented in forthcoming papers.

Physical Review AMar 1, 197427 citations

Coherence transfer between the 2P1/2 and 2P3/2 states in sodium, induced in collisions with helium atoms

M. Elbel, B. Niewitecka, L. Krause

The Hanle effect, which is commonly exhibited by atoms that emit resonance fluorescence while in a magnetic field, has been observed in sensitized fluorescence of sodium vapor. The sodium atoms were excited by σ+ polarized D1 radiation which produced a vector polarization in the 32P1/2 state, and were then transferred to the 32P3/2 state by collisions with helium atoms. The fluorescence was observed at an angle of 325° to the direction of excitation, and the magnetic field was perpendicular to the directions of the exciting and fluorescent light beams. The addition of helium resulted in the appearance of a circularly polarized D2 component in the fluorescent light. The polarization of the sensitized fluorescence decreased with increasing field as in the ordinary Hanle effect but the width of the Hanle signal was smaller than that observed in resonance fluorescence. The observed narrowing effect is in good agreement with theoretical predictions.The Hanle effect, which is commonly exhibited by atoms that emit resonance fluorescence while in a magnetic field, has been observed in sensitized fluorescence of sodium vapor. The sodium atoms were excited by σ+ polarized D1 radiation which produced a vector polarization in the 32P1/2 state, and were then transferred to the 32P3/2 state by collisions with helium atoms. The fluorescence was observed at an angle of 325° to the direction of excitation, and the magnetic field was perpendicular to the directions of the exciting and fluorescent light beams. The addition of helium resulted in the appearance of a circularly polarized D2 component in the fluorescent light. The polarization of the sensitized fluorescence decreased with increasing field as in the ordinary Hanle effect but the width of the Hanle signal was smaller than that observed in resonance fluorescence. The observed narrowing effect is in good agreement with theoretical predictions.

Canadian Journal of PhysicsDec 15, 197011 citations

Fluorescent emission of resonance lines at higher pressures

A. Jabeoński

Il Nuovo CimentoMay 1, 19532 citations

Collision-induced Hanle resonances in four-wave light mixing

N. Bloembergen

First, some historical comments on the Hanle effect and Kastler-type optical pumping are made. Next the recent history of the phenomenon of collision-induced coherences in optical four-wave light mixing experiments is briefly reviewed New experimental results on collision-enhanced Hanle-type resonances in the 3 2S1/2 ground state configuration of Na atoms in a buffer gas at high pressure are presented. The relationship between these optical fourwave experiments and Kastler-type optical pumping is pointed out.First, some historical comments on the Hanle effect and Kastler-type optical pumping are made. Next the recent history of the phenomenon of collision-induced coherences in optical four-wave light mixing experiments is briefly reviewed New experimental results on collision-enhanced Hanle-type resonances in the 3 2S1/2 ground state configuration of Na atoms in a buffer gas at high pressure are presented. The relationship between these optical fourwave experiments and Kastler-type optical pumping is pointed out.

Annales de PhysiqueJan 1, 19856 citations

J=2

level of a $J=1\ensuremath{-}J=2$ transition, the laser-induced Hanle effects keep a Lorentzian shape, independent of the laser intensity. For the $J=1\ensuremath{-}J=1$ transition, it is shown that the depolarizing relaxation processes play a leading part in the coupling induced by the laser between the transverse alignments of the two levels. On the other hand, the power broadenings of the Hanle effects are shown to be similar. For the

J=1

level of a $J=1\ensuremath{-}J=2$ transition, the Hanle-effect shape presents a departure from the Lorentzian one, owing to a coupling with the laser-induced hexadecapole moment in the

J=2

level. (ii) The populations of the levels exhibit a "zero-field saturation resonance" which is due to the coupling with the Zeeman coherences. These resonances, which reproduce the Hanle effects of the transition, can be observed on the $\ensuremath{\pi}$-polarized fluorescence from the levels. In general, these resonances appear as a saturation effect, i.e., they reduce the laser-induced fluorescence of the levels in zero magnetic field. However, for the ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$ transition, the ${J}_{a}=2\ensuremath{\rightarrow}{J}_{f}=2 \ensuremath{\pi}$ fluorescence presents an anomalous behavior; the saturation resonance increases the zero-field laser-induced fluorescence. The theoretical study shows the prominent part played by the value of the

{J}_{b}=1

level lifetime in the interpretation of this anomaly. Other results, such as the laser-induced depolarization of the fluorescence, are also obtained. All the theoretical predictions have been experimentally checked and will be presented in forthcoming papers.