Nonlinear effects in optical pumping of atoms by a high-intensity multimode gas laser. II. Exact theory for small angular momenta

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 $\sigma$-polarized laser and levels having small angular momenta. More precisely, I consider the laser transitions $J_b=1\mathrm{}\to J_a=0\mathrm{}$, $J_b=1\mathrm{}\to J_a=1\mathrm{}$, and $J_b=1\mathrm{}\to J_a=2\mathrm{}$. Two particular results are emphasized: (i) For $J=1\mathrm{}-J=0\mathrm{}$ and $J=1\mathrm{}-J=1\mathrm{}$ transitions and for the $J=2\mathrm{}$ level of a $J=1\mathrm{}-J=2\mathrm{}$ transition, the laser-induced Hanle effects keep a Lorentzian shape, independent of the laser intensity. For the $J=1\mathrm{}-J=1\mathrm{}$ 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 $J=1\mathrm{}$ level of a $J=1\mathrm{}-J=2\mathrm{}$ transition, the Hanle-effect shape presents a departure from the Lorentzian one, owing to a coupling with the laser-induced hexadecapole moment in the $J=2\mathrm{}$ 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 $\pi$-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 $J_b=1\mathrm{}\to J_a=2\mathrm{}$ transition, the $J_a=2\mathrm{}\to J_f=2\mathrm{} \pi$ 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 $J_b=1\mathrm{}$ 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.