We perform nonperturbative analysis of forward scattering of resonance laser light on atoms in magnetic field when the laser drives transitions between states with total angular momenta F=1,2 and study the role of the induced higher-order multipole moments in the forward-scattering signal. It is shown how the multipole moments affect these signals and why not all possible multipoles are revealed for some transitions. The analysis is performed in terms of density-matrix formalism and in terms of coupled and uncoupled (trap) states. Evolution of the trap states in a magnetic field is found to be responsible for specific dependencies of the forward-scattering signals on the multipoles of various ranks. The general theory is applied to the case of the Na
D1 line. We also present a pump-probe method for studying multipoles in systems with states of high angular momenta and with complex transitions overlapping within their Doppler width. \textcopyright{} 1996 The American Physical Society.
The forward-scattered light observed when a single-mode dye laser interacts with the three neon transitions 1 s 5 ( J = 2)-2 p s ( J = 2), 1s 3 ( J = 0)-2 p 5 ( J = 1), and 1 s 4 ( J = 1)-2 p 7 ( J = 1) has been investigated as an applied longitudinal magnetic field is varied. The 1 s 5 and the 1 s 3 states are metastable. This condition allows a comparison of the spectra for the cases 1 s 5 ( J = 2)-2 p 8 ( J = 2) and 1 s 3 ( J = 0)-2 p 5 ( J = 1) in order to discuss whether the complex line shapes obtained for the J = 2 to J = 2 atomic system are due to higher-order coherences or whether they originate from coherences between m = ±1 states. Experimental and calculated line shapes are presented. The calculations have been performed with the use of a semiclassical model for the light/matter interaction. A J = 0 to J = 1 (or a J = 1 to J = 1) model reproduces the overall shapes of the recorded spectra for all three transitions. The results show that, even when laser beam spatial effects and the sample isotopic effects are taken into account, interpretations of forward-scattering spectra in order to determine atomic parameters can reliably be done for simple J = 0 to J = 1 systems only.
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
Jb=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.
We present a theoretical study of double-resonance alignment magnetometers using linearly polarized light, in which the effect of atomic high-order multipole moments is considered. Starting from the effective master equation of our system obtained by eliminating the excited state adiabatically, we derive the full evolution equations of the atomic multipole moments. The analytic solutions of resonance signals involving the four-order multipole moments effect are obtained by using the perturbation approach. We present that the four-order multipole moments effect is negligible in the weak laser field, and the results reduce to that obtained by a three-step approach. However, the role of four-order multipole moments coupled by two-order tensor moments is more significant with the increasing Rabi frequency of light, which cannot be ignored. Meanwhile, the analytic expressions of relaxation processes are also studied, which are a linear combination of the laser-induced equivalent relaxation rate Γ L and the spin-exchange collision rate Γ g . The expected domain of validity of the three-step approach on light power is roughly given by Γ L < 1 2 Γ g . In addition, the steady-state results of resonance signals are presented in a strong radio-frequency magnetic field; in that case, the physical mechanism of the splitting of resonance signals is discussed. These results are valid for arbitrary light power and for an arbitrarily oriented static magnetic field.
The effects of magnetic optical activity in the sodium D1 line are investigated in detail both theoretically and experimentally. Particular consideration is given to the ultra-narrow Hanle-type features that are produced by the crossing of ground state Zeeman sub-levels and which although strongly exhibited by the F g =2 to F e =1, 2 doublet, are apparently absent from the F g =1 to F e =1,2 doublet. We demonstrate, quantitatively for the first time, that these features are principally a manifestation of Delta M=2 (quadrupole) coherences and are therefore not evidence for the existence of Delta M=4 (hexadecapole) coherences as originally proposed by Gawlik and co-workers (1987). Indeed the latter is shown to have little influence on these features even at light field intensities for which significant power broadening is observed. We also show explicitly that the width of these narrow crossing features is, for the typical vapour pressures used to give an optically thin sample, a function of the average time of transit through the light field. Using a simple phenomenological model we predict numerically both the absolute width of these coherence features and the rate at which they power broaden. Finally a brief consideration of the same coherence effects within the D2 line is presented.